Adding power via V8 or turbo, either way it is going to add weight up front.
I'd like to see pics, I don't see how this is possible. Maybe the BACK of the LS sits somewhat further aft (although 10" is still difficult to believe), the LS is a lot longer.
Understand your point about the massive T56, this could put engine/trans c.g. at a similar place to FA20 engine/trans c.g. location, but given the 2+2 configuration and the relatively forward engine location, the trans is still putting more weight on the front wheels than the rears.
Post them, of course.
If you were able to maintain stock weight distribution, or even improve it, congrats! But if there are other mods that help achieve that, please list them.
There are FD V8 swaps that have similar weight distribution to the stock 49/51, but like vs. like, with A/C, power steering, etc. weight moves forward about 1.5%.
I can't imagine the situation is any better with the FR-S, given how much further forward the firewall is relative to the front and rear wheels.