Theme INTERNATIONAL HARVESTER.  From a world of opportunities, Jeff Stillman has plucked four common, in-the-language two-word phrases, in which the first word is transformed from a pre-position modifier to a near-homophonic country name, which is also used as a pre-position modifier, yielding a new humorous phrase.   Not sure where Jeff is from. It's it's north of the border, this could be an example of Canada Dry humor.

17 A. European auto club device? : HUNGARY [HUNGRY] JACK.  From pancake mix to a tire-changing tool from my ancestral homeland.    Useful if you're hungry and tired.

27 A. Balkan primate? : GREECE [GREASE] MONKEY.  Not a car mechanic, but an inhabitant of the Athens Zoo.  Remember, monkeys, but not apes, have tales.

43 A. Mideast orchestral group? : QATAR [GUITAR] STRINGS.  Russia broke it's strings to tiny Qatar after an incident in 2011, but [presumably] the band played on.

 57 A. South Pacific 18-wheelers? : TONGA [TONKA] TRUCKS.  Not sure why, but this one is my favorite.   The kingdom of Tonga is a sovereign state comprising an archipelago of 176 scattered island, of which 52 are inhabited.   If you have a spare 14 minutes you can take this tour.  Toy trucks are optional.

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Hi gang, it's Jazzbumpa, your tour guide for today.  Can't say I'm a big fan of globalization, but let's grab a GPS and see where Jeff takes us.

Across

1. Middle Ages century opener : MCCC.  First stop, a long time ago - the beginning of the 14th century.  From what I've read, a thoroughly dismal time - even before the plague.  Let's move on.

5. Request before a snap : SMILE.  That's more like it.  Say "cheese."

10. "Survivor" airer : CBS.  Never watched it, but it's on some remote island out there - right?

13. Something to assume : ALIAS.   An assumed name, like Jazzbuma.

15. Foofaraws : TODOS.  Do you think a play called "Much Foofaraw about nothing" would still be popular more than CD centuries later? 

16. You can dig it : ORE.   Also called "pay dirt."  Your ORE or mine? 

19. Floor application : WAX.  A protective coating that makes your floor shine.

My beautiful floor
I do adore
How it shines
Much more brightly
Than before

Or do you abhor 

when I WAX poetic?

20. Pronouncement of Pontius Pilate : ECCE HOMO.  "Behold the man."  Thus spake he when presenting the scourged and thorn-crowned Jesus to a hostile crowd. [John 19:5]

21. Device commonly used in "The Twilight Zone" : IRONY.   According to the Free Dictionary, dramatic irony is "The dramatic effect achieved by leading an audience to understand an incongruity between a situation and the accompanying speeches, while the characters in the play remain unaware of the incongruity."

23. "Citizen Kane" studio : RKO.  Radio-Keith-Orpheum.  Any connection to Radical Keith Olbermann remains unproven.

24. One-time ring king : ALI.  Nee Cassius Marcellus Clay, Jr.   Laila's dad.

25. Raise objections : DEMUR.  I'd be reluctant to disagree.

31. Vegetation : FLORA.  Generally referring to a regions native plant life.

34. Butts : RAMS.  Strikes against something with a blunt object.  Lest anyone DEMUR, I'll refrain from drawing any connection to 51 D.

35. Julio's "that" : ESA.  That's in Spanish

36. Yokel : RUBE. 

37. Mythological do-gooder : FAIRY.  Hmmm.  Only sometimes.  Fairy godmothers, for sure.  But isn't there always a catch?

39. Word-of-mouth : ORAL.  Tell me about it.

40. "Star Trek" rank: Abbr. : ENS.  Ensign - currently a commissioned rank in the U.S. Navy or Coast Guard that is below lieutenant junior grade.  Presumably something similar in the star fleet.

41. Greenhouse square : PANE.  Ultimately from the Latin pannus, the same source as "panel." A greenhouse is a framed structure with mostly glass walls.  A piece of flat glass is called a PANE.  Regularly sized squares are relatively easy to work with.  It all fits.

42. Matter to debate : ISSUE. 

47. Who's who : ELITE.  The A-list.  After recently watching Les Miz and as much of Vanity Fair as I could stomach, I'm rather down on the ELITE.

48. One of the Bobbsey twins : NAN.  The LW informs me there were two sets of twins.  Can you name them?  I sure can't.

49. __ double take : DO A.  Look and look again.  This happens when you look at one twin and then the other.  Or at the first one twice.  And why not?

52. "Come here __?" : OFTEN.  Classic pick-up line, not likely to work with the twins.

54. Losers : ALSO RANS.  Perhaps guys who use lousy pick-up lines

56. Expected result : PAR.  Like avoiding bogeys on the golf course, or going home from the bar alone.

60. Counterterrorist weapon : UZI.  Since being introduced in 1950, this family of sub-machine-guns has been widely used by military, police and special forces.  This clue suggests that the bad guys don't have any.  Hmmmm.

61. "__ Heartbeat": Amy Grant hit : EVERY.  Very 80's looking vid, but it's from 1991.

62. One handling a roast : EMCEE.  I've done this a few times at retirement parties.

63. Jiff : SEC.  Jiffy, second - quickness indicators.  I'm trying to come up with a Jif and violence joke, but peanut butter doesn't seem like much of a weapon.

64. Indian tunes : RAGAS.  Brought to the U.S by Norah Jones' dad.  Here is a 4:47 example.  Not an ear worm, as far as I can tell.

65. Makes, as a visit : PAYS.  But we did get to PAY a virtual visit to India.

Down

1. "Real Time" host : MAHER.  Notorious iconclast, not well known for his tasteful routines.

2. Coop sound : CLUCK.  Chicken coop.

3. Dos y tres : CINCO.  Two plus three = 5.  Más español.

4. Batting practice safety feature : CAGE.  I wanted to link the batting cage scene from Bull Durham, but no dice.  Moneyball?  Nope.  We have to settle for this.

5. Buffalo : STYMIE.  Buffalo, as a verb means bamboozle, dupe, deceive, trick.  STYMIE means stand in the way of, present an obstacle.   Wrong turn here - these are in no way equivalent.

6. Magic charm : MOJO.  Or a spell, hex, or more broadly, magic power.

7. Craters of the Moon st. : IDA.  Craters of the Moon National Monument is located in the State of Montana.

8. __ cit.: footnote abbr. : LOC.  "In the place cited."  Refers to a repeat reference to the the same page in a previously cited work.

9. Native Alaskans, historically : ESKIMOS.  The native Alaskan and other Arctic cultures across Siberia and North America have been in place for over 4,000 years.

10. Water cooler gatherers : COWORKERS.  In my office it was a coffee maker.  Perps gave me COW, and that caused all sorts of mayhem.

11. Muffin mix stir-in : BRAN.  A source of healthful fiber.

12. Hot : SEXY.  Here's a collection for the ladies.   With a zoom feature.

14. 1943 war film set in a desert : SAHARA.  Starring Humphry Bogart as a tank commander in Lybia.  WE really are convering a lot of ground.

18. Play thing? : ROLE.  Clever - an actor's part in a play.  My grandsons had small roles in Les Miz, and they both died on the barricade.  That was hard to watch.

22. Bolt : RUN.  But I sat through it, and didn't bolt.

25. Letter opener? : DEAR Sir, Madam, Santa, John, etc.

26. Acting award : EMMY. For TV acting.

27. Coll. senior's test : G R E  Graduate Record Exam.

28. Old-time news source : CRIER.  I just had this one on Jan 16th, so I'll repeat what I said then.  An official whose duty is to make public announcements. A bit passé these days, but several municipalities in North America, Australia and New Zealand still have Town CRIERS. Should I be disturbed that the first answer I thought of was DRUNK? It fits.

29. Biblical twin : ESAU.  Older than his brother Jacob, he sold him his birthright for a bowl of stew.  The transaction is not known to have involved chewing gum.

30. School with the motto "Lux et veritas" : YALE.  Light and truth.  Yale is home of the Eli's and the Skull and Bones.  If this is a secret society, then why do I know about it?

31. It's measured in Hz : FREQ.  Herz and frequency. 

32. Roman moon goddess : LUNA.  And my favorite HP character.

33. Relating to childbirth : OBSTETRIC.  The long form of OB.

37. Like some clocks : FAST.  Are you satisfied with this clue?

38. First few chips, usually : ANTE.  I do like this one, for an X-word stalwart.

39. Org. in old spy stories : OSS.  Office of Strategic Services.  Precursor to the CIA.  I wanted KGB.

41. HP product : PRINTER.

42. Overlook : IGNORE.

44. Tankard filler : ALE.

45. Puts down, as parquetry : INLAYS.  Some examples.

46. Harper's Weekly cartoonist : NAST.  Thomas, 1840-1902.  He gave us the modern image of Santa Claus and the Republican party elephant.

49. Bangladesh capital, old-style : DACCA.  Another exotic stop on our trip.

50. Pitched perfectly : ON KEY.  Every trombonist's ideal.

51. Toting team : ASSES.  Do you assess a team of asses by their toting ability?  Why, yes.

52. Musical number : OPUS.  A composers works are cataloged with OPUS numbers.  Except for Bach.  He gets BWV  (Bach-Werke-Verzeichnis) designations.

53. Throw for a loop : FAZE.  This is as good a time as any to admit I had a lot of trouble with this puzzle

54. Uttar Pradesh tourist city : AGRA.  Home to the Taj Mahal, as I learned form crosswords.  We are covering a lot of ground.

55. __ roast : RUMP.   A cut of meat from the hindquarters of the animal - cattle, not asses.

58. Eggs, in old Rome : OVA.  Ova and out?  Not quite.  One more stop.

59. Not pos. : NEG. Positive and negative.  Are you charged up by these abreviations?

Well, here we are back home.  Hope you enjoyed the trip and will fly with us again some time soon.  B'bye.