Completed!
Thanks to feelinferrety, Deusovi and ffao in The Sphinx's Lair for helping solve the trickier ones!

Clues:
Surrounding trapped center with force! (8)
WRAPPING &lit is WR(APP)ING
Small dog and cat must act under control of others (6)
PUPPET "must act under control of others" is PUP + PET
No better after leaders now shout all the time (7)
NONSTOP "all the time" is NO + N_ S_ + TOP
$\hspace{9em}$ (thanks @Deusovi in TSL for solution)
Loud chaotic shows cannot be improved (8)
FLAWLESS "cannot be improved" is F + LAWLESS (what does "shows" do in wordplay?)
Educated intellectual gained additional knowledge (7)
LEARNED (ddef.)
Fraud perpetrator who primarily supports artwork (6)
WEASEL "fraud perpetrator" is W_ + EASEL
Castle protects some revolutionary, most importantly (8)
FOREMOST "most importantly" is FOR(EMOS<)T
Extremely blissful place is part of exhibit (8)
PARADISE "Extremely blissful place" is PARAD(IS)E ("IS" part of ...)
Legal documents permit ship docking areas (9)
PASSPORTS "legal documents" is PASS+PORTS
Wild ape hits chest with extreme effort, ending half-truce (5,8)
PEACE OFFERING "half-truce" is (PEA)* + C(E_)OFFER [end]ING
$\hspace{9em}$ (thanks @ffao in TSL for wordplay)
Deformed dog without tail is followed by insect (6)
MUTANT "Deformed" is MUT_ + ANT
Earlier versions are ultimately failures after eons act recklessly (9)
ANCESTORS "Earlier versions" is (ANCESTO)* + R + _S
Inclined to handle an educated prisoner (6)
LEANED "Inclined" is ...[hand]LE AN ED[ucated]...
$\hspace{9em}$ (thanks @feelinferrety in TSL for wordplay)
A surrounded pound incorrectly sorts under three (9)
ALBATROSS "under three" (from golf) is A(LB)A + (TROSS)*
Summaries in turn summarized initially create separation (7)
SPACERS "create separation" is (SPACER)< + S_ ("They create separation" is better?)
Attacks almost come alongside backstab (7)
COMBATS "Attacks" is COM_ + (BATS)<
Advanced condition frequently near center of the body (5,2,3,3)
STATE OF THE ART "Advanced" is STATE + OFT + HEART
Frigid morning is piercing, new (8)
UNAMUSED "Frigid" is UN(AM)USED (AM piercing ...)
Too much prayer restricts god (8)
PLETHORA "Too much" is PLE(THOR)A
Surely you won't start after greeting blunt outsiders (2,5)
NO DOUBT "Surely" is NOD + [y]OU + B[lun]T
Cardinal number 5 before 0 essentially totals 50 (7)
PIVOTAL "Cardinal" is PI + V + O + [to]TA[ls] + L
Direct quote's middle lines are extreme (7)
OVERSEE "Direct" is [qu]O[te] + VERSE + [ar]E
Weird new rants get abbreviated (7)
STRANGE "Weird" is (STRAN)* + GE_
Setter's breathing issue reportedly results in unpleasant smell (6)
MIASMA "unpleasant smell" is {MY ASTHMA}→hom.
"Follow reply" becomes a feature (6)
ASPECT "feature" is {RE becomes A}SPECT
$\hspace{9em}$ (thanks @Deusovi in TSL for wordplay)
26a. Decrepit side street cut short (6)
DESIST "cut short" is (DESI)* + ST
$\hspace{9em}$ (thanks again @feelinferrety for SIDE*)
26d. Yes, Russian hail ruins flower (6)
DAHLIA "flower" is DA + (HLIA)*
"Average heart," reads diagram's section (9)
PARAGRAPH "section" is PAR + [re]A[ds] + GRAPH
With one another for the purpose of finding her (8)
TOGETHER (ddef.)
Relaxed elderly meditated at first; that is, knitted and didn't move (8)
REMAINED "didn't move" is R_ E_ M_ + {IE knitted with AND} → AINED
Comments:
Whew — some of these clues were really tough!
The clues were very nicely constructed and used a great mix of indicators and misdirection, which made solving each one feel like a victory. The relative sparsity of crossing letters made a couple of these feel like a stab in the dark, but I don't even think that's a weakness - it just amps the difficulty up some more, adding further to the sense of accomplishment at completion. I must say that the clues were hard enough that, even "knowing" the answers to a few, I got stuck on the wordplay for a while - and on some, it took some help from the folks in TSL to actually see how they worked; solving completely solo would be a monumental endeavor. But, since that's how a lot of puzzles here end up being solved, that just adds to the fun. :)
Thanks for sharing these terrific clues with us!