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ACROSS

 1 Prepare cured eel’s head to lose weight (6)

 4 Give a hearing to a scrappy Native American (6)

10 Doc [that’s what it says here] is involved in any hip replacement (9)

11 Lead soprano role in a Puccini opera about an ape (5)

12 Rumba dancing in Myanmar (5)

13 Bend down if I’d sounded dopey (9)

14 Happy drummer loses head, takes an excessive amount of drugs, and trips
  out when eating pie filling (2,4,7)

18 Grumpy, brusque, and embarrassed about Arizona city (5-8)

24 Alien I find deft and bashful (9)

25 Small dog with one large student (5)

27 Excuse tabloid bait, ignoring the odds (5)

28 Consequently, a set of letters associated with 6 days of penitence
makes you sleepy (9)

29 Appreciate joke, when Jack leaves a summary (6)

30 Yes, Zen paradoxically… wait! This word was supposed to be in a clue, not
  in the diagram! (6)

DOWN

 1 Name exotic club outside capital of Italian nation (8)

 2 10 eating bread, perhaps with less butter (5)

 3 City’s stylish past (7)

 5 Ancient city’s ceremonial display at the inauguration of Edward the Second
  (7)

 6 Carom wildly, captivating young female official (9)

 7 Company in desperate need to make something hard to read (6)

 8 Gets up to embrace beginning of natural hair treatments (6)

 9 Certain cubist has nightmares (6)

15 It’s not likely the female principle, separating thousands, is turning to vapor
  (9)

16 and 26 Rose accepts Biden’s ascent as a personal irritant (3,5)

17 I really make an effort to limit Western city’s fetishism (8)

19 “Ring is ring” is wrong, for starters (7)

20 That group’s clothing is an alternative to 17 (6)

21 Bury Benjamin and Thomas, with the former’s head at the latter’s foot (6)

22 Common accompaniment for film erotica enthralling crooked cop (7)

23 You may have to have it when buying alcohol or mixing acid on road (2,4)

26 See 16

SOLUTION TO PUZZLE NO. 3369

ACROSS 1 SCA(FFO)LD (off rev.) 5 pun 10 VI + R + GO 11 anag. 12 B(AP + TIZ)ED (zit, Pa rev.) 13 SUED + E 15 PAR(O + L)ED 18 AL + READ + Y 19 RUM[p] 20 CHIM[p] + ERA 22 POP(U)LAR 24 CA + STS 25 HAR(BORE)D 29 D(ROME + DA)RY 30 A TOLL 31 TA(M)ING (giant anag.) 32 anag.

DOWN 1 S + AVE 2 A(O)RT + A 3 F(RON)TAL (flat anag.) 4 LAP + AZ 6 anag. 7 anag. 8 L(UMBER + Y)ARD 9 anag. 14 SPAC + ECA + DET (rev.) 16 [b]RAINSTORM 17 anag. 21 E + AS + TERN 23 “pro-pain” 26 rev. hidden 27 EPOC (rev.) + H 28 F + LIP