Endless party… famous last words

Question

Twelve of the clues are missing song titles, all different from one another, substituted by boldface question marks, one question mark per word. Each missing song was, as a single, in the top ten in the U.K. or the U.S. (or both). The twelve songs have something else also in common, as you'll discover in the course of solving the puzzle.

Across

1. Without a tee, golf better than, say, poop (6)
4. Drum and guitar innovator! (7)
9. Until ? ? eats starters (3)
10. Style or theme: it can be proven (7)
11. A red metal penny is missing (3)
12. Table provided supper, after lunch was sent back (5)
14. In SoundCloud, "An Apostle" (4)
16. A cheese setback? (4)
18. Perhaps Princess Fiona returns without her ultimate self-esteem (3)
19. God of mourning (5)
21. Renal failure study (5)
23. Drummer's groin operated upon (5)
24. Governor of North Carolina and New York is fit (5)
25. ? ? ? at first: precisely when? (3)
27. For present, first of talkies follows moving picture (4)
29. Sergeant Major? (4)
31. Rank among fruit (5)
33. Endless party for a scripting language (3)
34. An anticoagulant, it's in a box (7)
36. ? ? message (as yet unknown) (3)
37. Speak to a ? ?, perhaps? (7)
38. Eliot Canyon has echo (6)

Down

1. Supposed to arrive ?, e.g., to ham it up for the audience (7)
2. ? ? ? lasts only part of a leg (3)
3. Say famous last words in reverse before king (5)
4. It's cold outside of Bangor! Taking a bit of rum (3)
5. ? ? with her head between her feet for a group of soldiers (4)
6. Perhaps was like a Princess Zelda melee (5)
7. Sleep among dugongs and manatees (7)
8. "Little ? at last," cry (4)
13. Father now formed a glower (5)
15. Having an argument is high-class — not (5)
17. Develop ? ? without an end (4)
19. Find uneven support (4)
20. Opening ration without a shake (5)
22. Moravians hide, maybe like magpies (5)
23. Objects, including crown, of grandeur! (7)
26. March: time for film (7)
28. A lie worded ? ? ? ? (5)
30. ? ? ? with a bread (4)
31. Monsieur Gainsbourg's genre? Pah (5)
32. Top expert bored by Masonic initiation (4)
35. It's an insect, ? ? (3)
36. Endless Story Hill (3)

Answer 1

The completed grid, with some relevant entries highlighted:

Answers, explanations, clues with song titles inserted:

Across
1a. OUTPUT OUTPUT(-t) Without a tee, golf better than, say, poop (6)
4a. BEATLES BEAT + LES (Paul) &lit Drum and guitar innovator! (7)
9a. ERE first letters Until Eleanor Rigby eats starters (3)
10a. THEOREM ORTHEME* Style or theme: it can be proven (7)
11a. ZIN ZIN(-c) A red metal penny is missing (3)
12a. DEFER RE-FED<< Table provided supper, after lunch was sent back (5)
14a. PAUL homophone of PALL In SoundCloud, "An Apostle" (4)
16a. EDAM MADE< A cheese setback? (4)
18a. EGO OG(-r)E< Perhaps Princess Fiona returns without her ultimate self-esteem (3)
19a. SHIVA ddef God of mourning (5)
21a. LEARN RENAL* Renal failure study (5)
23a. RINGO GROIN* Drummer's groin operated upon (5)
24a. TRY ON ddef (William Tryon) Governor of North Carolina and New York is fit (5)
25a. IFF initial letters I Feel Fine at first: precisely when? (3)
27a. GIFT T follows GIF For present, first of talkies follows moving picture (4)
29a. JOHN first name of famous people called Sergeant and Major Sergeant Major? (4)
31a. MANGO AMONG* Rank among fruit (5)
33a. LUA LUA(-u) Endless party for a scripting language (3)
34a. CITRATE IT in CRATE An anticoagulant, it's in a box (7)
36a. TBA substring Get Back message (as yet unknown) (3)
37a. ADDRESS? A D DRESS Speak to a Day Tripper, perhaps? (7)
38a. GEORGE E in GORGE Eliot Canyon has echo (6)
Down
1d. OVERDUE homophone of OVERDO Supposed to arrive Yesterday, e.g., to ham it up for the audience (7)
2d. TOE last letters Ticket to Ride lasts only part of a leg (3)
3d. UTTER (ET TU)< + R Say famous last words in reverse before king (5)
4d. BRR B(-ango)R + R(-um) It's cold outside of Bangor! Taking a bit of rum (3)
5d. ARMY MARY with M moved between R and Y Lady Madonna with her head between her feet for a group of soldiers (4)
6d. LAZED ZELDA* Perhaps was like a Princess Zelda melee (5)
7d. SANDMAN substring Sleep among dugongs and manatees (7)
8d. WEEP WEE + (-?)P "Little Help at last," cry (4)
13d. FROWN FR + NOW* Father now formed a glower (5)
15d. UNARY U+NARY Having an argument is high-class — not (5)
17d. PLAN P LAN(-e) Develop Penny Lane without an end (4)
19d. SPOT S(-u)P(-p)O(-r)T Find uneven support (4)
20d. INTRO R(-a)TION* Opening ration without a shake (5)
22d. AVIAN substring Moravians hide, maybe like magpies (5)
23d. REGALIA G in REALIA &lit Objects, including crown, of grandeur! (7)
26d. FOOTAGE FOOT+AGE March: time for film (7)
28d. FRAUD FRAMED with ME replaced by U A lie worded From Me To You (5)
30d. NAAN NAN containing A She's A Woman with a bread (4)
31d. MYEYE M + YE-YE but surely should be (2,3) not (5) Monsieur Gainsbourg's genre? Pah (5)
32d. ACME ACE containing M Top expert bored by Masonic initiation (4)
35d. TIS (-man)TIS It's an insect, Nowhere Man (3)
36d. TOR (-s)TOR(-y) Endless Story Hill (3)

Credit and thanks where due:

Jeremy Dover pointed out the intended song for 37a. (I had considered it but rejected it for the reasons above -- but Jeremy was right.) Jafe pointed out the right parsing of 12a, where I'd missed a key point. Jafe suggested the correct answer for 36a, which I hadn't considered; the song suggestion above is mine. msh210 kindly confirmed these people's suggestions, and also gave a hint for 28d.