The Crossword Centre

 I am the Eggman by Henri - Solution

Dots replacing the nine letters omitted from clues form a 3x3 square in the middle of the grid. Omitted letters rearrange to INVENTIVE, here meaning "thinking outside the box". Twelve answers are too long for their grid space and extend beyond the edges of the grid, spelling SAM LOYDS DOTS, referring to 'Nine Dots’ (original name: ‘Columbus Egg Puzzle’), a classic mathematical puzzle that is the origin of the phrase "thinking outside the box”. Solvers must solve the Nine Dots puzzle, i.e. draw four straight lines connecting the dots in a single pen stroke. There is more than one correct solution but they all involve moving the pen beyond the space bounded by the nine dots. 

 Across 1 Pluto gave birth to last couple of puppies HADES Pluto / HAD + ~ES 5 King casually unravelling blue garment CHASUBLE garment / CHAS + BLUE* 11 Preserving unfinished juniper [S]AVIN juniper / SAVIN(g) S 13 Digital complaint related when the Italian overwrites note AGNAI[L] digital complaint / AGNA(te>IL) L 14 State of Poles transporting packet around America MASSACHUSETTS state / MAS_TS around (SACH(US)ET) 15 Live next to abandoned historical church BETHEL church / BE _ H_~L T, E 17 In their opinion, not having husband as idol [T]OTEM idol / TO T(h)EM T 18 Irrational, disturbed and dismissive of outsiders, grim old Indian criminal PINDARI old Indian criminal / PI + AND* + (g)RI(m) 19 Pertaining to pill box, nothing missing IN RE pertaining to / INR(o) _ E 20 No place to go NIP to go / N_P I 21 Formerly timeless work by Baudelaire? VERS work by Baudelaire? / _ERS(t) V 24 Figures in play area know, according to Ed and Bob RECKONS figures / REC + KON + S 27 Relation not totally helping RATI[O] relation / RATIO(n) O 29 Motorists like pineapple ANANAS pineapple / A_A + _ AS N,N 31 Leisure facility featuring Milo performing MINIATURE GOLF leisure facility / (FEATURING MILO)* 32 More like cereal I ate or prepared [O]ATIER more like cereal / (I ATE OR)* O 33 Everyone starts to overstate your temper ALLO[Y] ALL + O~ Y~ Y 34 Recent union member, of necessity, going around with superficially lazy women NEWLYWED recent union member / NE(W+L~Y+W)ED 35 Fibre in grains is altered SISAL fibre / (grain)S IS AL(tered) Down 1 Drive away to protect Australian politician getting clean [S]HAMPOO clean / SH(A+MP)OO S 2 A Vatican City soldier, one being forward AVANTI forward / A + V + ANT + I(s) 3 Sack from governing body senior officers on hill above court house DISBENCH sack from governing body / DIS + BENCH 4 Maybe David succeeded with Greek character STATUE maybe David / S + TA_U_ T,E 5 Almost completely hide hereditary laugh... CACHINNATE laugh / CACH(e) + INNATE 6 ... it's hard enough being discontented HEHE laugh [see 5d above] / H + E~H _ E 7 Nomadic hunter captures small antelope SASIN antelope / SA(S)N I 8 Soothsayer announced something that's boring [A]UGER something that's boring / “AUGUR” A 9 Sell up? Not I, not yet LATER not yet / RETA(i)L< 10 Writer lives on greeting cards [M]EISHI cards / ME + IS + HI M 12 In Nice you made up story, 'eating fruit like a French Bulldog' TULIP-EARED like a French Bulldog / TU + LI(PEAR)ED 16 Rosa's pal rocking shades PARASOLS shades / (ROSAS PAL)* 21 Grape Farmers Institute, extremely eager society VINERS grape farmers / _I + _ E~R + S V,N 22 Perhaps McCartney once to legally establish academy STELLA perhaps McCartney / STELL + A 23 Put penny on 'Skinny Lord' to get a pound PINFOL[D] pound / P + INFO + LD D 24 Send back bishop possibly held by communist REMAN[D] send back / RE(MAN)D D 25 Start to enjoy low-calorie cream ELITE cream / E~ + LITE 26 Egg supplier in row over end of subsidy OVARY egg supplier / O_AR + ~Y V 28 Doctor Lewis Eddies in Dundee WIEL[S] eddies in Dundee / LEWIS* S 30 Microwave instrument NUKE microwave / _UKE N