Wow, yeah that is alot of overbore. 3.875" stroke (396 with .030" overbore), 402 with .040" and that would be a full .060" overbore which requires sonic checking on an LT1 block.
I would be happy with a 383 myself, 396 can be done for not TOO much more money, and I guess its not THAT much stroke when you look at some other GM vehicles, but a 383 would make plenty of torque down low and the rings would last you a little bit longer (and less block clearancing). You WILL need an aftermarket pan with a 396, some 383 cranks fit in a stock pan with some hammering, but the stock pan really should be replaced anyway, especially if you road race, but even a drag car would benefit from better oil control, especially with the longer stroke making crank whippage more a problem.
You could even build a 421 cube LT1, but you can believe that gets expensive.