Builder,
You can get a 377 from a 350 block, you just have to use a 400 crank and not bore the block, hence a 377.
I presently have a 377 in my 73 Camaro, it's a high revving version redline at 7800 though have had it to 8200 by accident. It's a good running motor and would do very well in a light car like you intend to build. I don't have all of the good stuff you plan on putting in the one you intend to build. I am running a 4 bolt 400 block, stock forged steel chevy crank and stock rods that were polished and shot peened. Running flat top forged full floating pistons, Victor Jr. Heads and super victor intake, topped by a 750 carb shop double pumper holley. Have a lunati cam 260 intake duration and 266 exhaust duration with .640 lift with 1.6:1 rockers, and lifters, driven by a pete jackson gear drive, the quiet one.
To get the power you want out of the 377 your gonna have to go with a really stout compression ratio or supercharge it. A blower is much more streetable depending on boost. It's a whole lot easier to get the kinda HP your looking for with a big cubic inch motor, such as a crate 572 from chevy, and you could probably be in about the same price range as building the 377 to that kind of HP. The streetable version of the 572 has 620 HP and the race version has 720 but you have to run race fuel as the compression is up there, think it's 13 to one.
I regret not putting a bigblock in my car all of the time.
Another option is one of the stroked up small blocks, I've seen them as high as 455 cubic inches, but that's pushing the limit on the block and all of those other moving parts.