The addition of the overlaps made for an amusing diversion; on the other hand, it strongly dictated the order of solving, which was to attack down clues as much as possible before working on the accrosses.

Down clues are normal. Each across clue, except 30, leads to two words which overlap, the last three letters of the first being the first three of the second. The overlaps occupy the central section of the diagram, bordered left and right by broken bars. Each across clue consists of clues to the two overlapping words, in either order; one of these is normal, but in the other the cryptic indication refers only to the full word minus the overlapping portion. Either of the two overlapping words may be clued first, and the two types of clue that make up each double clue may be in either order.

Let's see if I can represent the solving process clearly enough, with the power of colour!

  • 1ac: OVERSHOTCHPOT: Again, host subtly exceeded mutton broth, cold, with warm round bit of polenta (8, 8): OVER (again) + *(HOST) C(old) + HOT (warm) round P(olenta)
  • 11ac: PERICOPERABLE: Fit to function after visit to theatre, a rebel reread church extract, fine following page (8, 8): P(age) + ERIC (fine) OP (visit to theatre) + *(A REBEL)
  • 14ac: TRASHCANICULA: Destination for junk star guided by height the moon turned in about star (8,8): *(STAR) + H(eight) LUNICA (moon) reversed in CA (about)
  • 16ac: MODULATELIERS: Earliest stirring in workshops to adjust subject of painting for all to see shifting base? (8, 8): MODEL - E (base) + U (for all to see) *(EARLIEST)
  • 18ac: YESTEREFA: Forbidden meal interrupted by whistle-blower – last, for sure (6, 6): YES (for sure) TEA (meal) outside REF (whistle-blower)
  • 23ac: TEAPLANTHEMIA: Commercial bush, petal trained by worker, reverse of ideal alongside border plant-forms in art (8, 8): *(PETAL) + ANT (worker) AI (A1, ideal) reversed after HEM (border)
  • 29ac: IVORIESTONIAN: Like e.g. Cameron once welcoming southern European national, perhaps warn one going after bit of ice creamier than the rest? (8, 8): I(ce) + VOR (perh. warn, Shakesp.) + I (one) ETONIAN (like David Cameron in school days) around S(outhern)
  • 30ac: SEMANTRABEATE: Bell equivalents; built of horizontal beams (8, 8)
  • 31ac: TRUDGINGULFED: Overwhelmed, nursing damaged lung, I took food, making slow progress with date in fruit basket (8, 8): D(ate) in TRUG (fruit basket) I FED (took food) around *(LUNG)
  • 1dn: OPTOMETRIST: Work on volume once causing grief for eye expert (11): OP (work) + TOME (volume) + TRIST (obs. grief)
  • 2dn: VERBOSE: Wordy book’s half in poetry (7): BO(ok) in VERSE (poetry)
  • 3dn: RISQUE: Queen captured in revolt? Danger past (6): QU(een) in RISE (revolt)
  • 4dn: SCHI: First of snow covering hills, I ski in Oberstdorf (4): S(now) C(overing) H(ills) + I
  • 5dn: HOCK: Wine jar, not the first (4): (s)HOCK (jar)
  • 6dn: TENDER: Painful? It’s often de rigueur in part (6) ofTEN DE Rigeur
  • 7dn: CRIBLE: Dotty translation (too literal?) given with the French, ignoring accent (6): CRIB (literal translation) + LE (fr. “the”); “ignoring accent” to deal with the acute in “criblé”
  • 8dn: HACK: Pick mercenary, but lacking old gun (4): HACKBUT (old gun) - BUT
  • 9dn: OLLA: 50% of TV comedy served up in miscellany? (4): the TV comedy is 'Allo 'Allo!
  • 10dn: TEARSTAINED: Wretchedly triste, Danaë may appear so? (11): *(TRISTE DANAE) &lit.
  • 12dn: RANDY: Tomboy exhibiting extremes of roguery (5): extremes of “roguery” are R AND Y
  • 13dn: BUTE: Evidence of horse-doping? Objection leading to ending of licence (4): BUT (objection) + (licenc)E
  • 15dn: ATTENDS: Marks & Spencer initially stocking alcohol-free wine, without success (7) AND (&) + S(penser) around TT (alcohol-free) + WINE - WIN (success)
  • 17dn: RUINATE: By implication, a true Shakespearean smash? (7): A TRUE = RU IN ATE
  • 19dn: SLUING: At home, in grip of strong drink, spinning uncontrollably (6): IN (at home) in SLUG (strong drink)
  • 20dn: TAPETI: Rabbit from part of SE Asia that’s indulged in (6): TAI (part of SE Asia) with PET (indulged) in
  • 21dn: FENNEL: Herb names one has instinct about (6): NN (names) with FEEL (instinct) around
  • 22dn: AMNIA: Fluid containers? It’s madness switching first couple (5): MANIA (madness) with first two letters swapped
  • 24dn: ATOM: Anything tiny, of matter principally (4): A(nything) T(iny) O(f) M(atter) &lit.
  • 25dn: AVER: Old Scots nag, mean, ageless (4): AVERAGE (mean) - AGE
  • 26dn: GRAD: Successful finalist, task over (4): DRAG (task) reversed
  • 27dn: STAG: Grass? It’s cut short among spinach (4): T (it, shortened) in SAG (spinach)
  • 28dn: ZOBU: Cross male, Unionist sketch writer sent up (4): U(nionist) + BOZ (sketch writer; ref. Boz) reversed