How do I make a 700R4 survive behind an LS in a square body?

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

• TCI warns that incorrect TV-cable hookup can burn the 3-4 clutch pack in as little as 5 miles of driving. (LS1Tech)
• Bowler lists a GM 700-R4 package rated up to 450 lb-ft with components including a wider 2-4 band, Corvette servo, Sonnax Smart Shell, steel-sleeve input drum, Transgo shift kit, wide sun-gear bushing, extra-wide rear planet, hardened pump rings, upgraded separator plate, 13-vane pump and extra clutch plates (a 550 lb-ft build is also listed). (Bowler Transmissions)
• Bowler's Tru-Shift article states that the vast majority of 700R4 problems come from misadjusted TV cables rather than bad builds, because 700R4s live and die by line pressure. (Bowler Transmissions)
• ChevyHardcore notes TCI's Constant Pressure Valve Body still requires the TV cable to operate the shifts, but reduces the risk of failures caused by low line pressure. (Chevyhardcore)
• Hot Rod's example swap used a Phoenix 'SS' 700R4 rated at 450 hp and 500 lb-ft, built with high-load sprags, high-energy friction and band, and increased pump volume and pressure; the package included a high-performance lockup converter, COMPUSHIFT Mini, G-Force crossmember, Lokar TV cable and Demon correction bracket. The article lists 700R4 ratios as 3.06:1 first and 0.70:1 overdrive (versus 2.52:1 first for a TH350). (Hot Rod)

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