What part numbers cover flexplates for a 700R4 behind a big block?

Here is what the documentation says. Each point links to its source; details depend on your exact computer, harness and transmission.

• Advance Adapters states the typical recessed Gen III LS crank flange sits about 0.400 inch closer to the block, and that mating an LS to a TH350/TH400 requires an LS-compatible flexplate, crank spacer and 11 mm flexplate bolts; its listed parts are 716141A (11 mm flywheel bolts), 711500A4 (LS-to-TH350/TH400 flexplate) and 716155A (crank spacer bushing). Exclusions include LS7/LS9/LSA/LSX eight-bolt cranks, Gen V 2014+ engines, certain non-recessed iron-head 6.0 engines, and 1999-2003 4.8 engines originally mated to manuals. (Advanceadapters)
• Dirty Dingo's LS flexplate kit fits TH400, 4L80E and aftermarket dual-pattern TH350/700R4 converters on 2002-and-newer Gen III/IV LS engines; it is built for an 11.5-inch converter bolt circle and includes a custom 168-tooth internally balanced steel flexplate, crankshaft spacer and correct-length ARP flexplate bolts, with the spacer compensating for the LS crankshaft being about 0.400 inch shorter. (Dirtydingo)
• Dirty Dingo explicitly states its kit will not work with stock TH350 or 700R4 torque converters, and will not fit 1999-2000 6.0L engines with a 0.400-inch extended crank flange and factory flat flexplate, 1999-2000 4.8L engines originally equipped with a manual transmission, or 1999-2001 LS applications with a 0.400-inch extended crank flange. (Dirtydingo)

Confirm against the instructions for your exact parts before wiring. More: Transmission control in our tuning guide.