Does anyone know how much the side panels would have to be moved in towards the center of the car?
That's directly related to how much you want to move the inner wheelwells inboard. The interior side panels butt up against the inside edge of the inner wheelwell at the bottom of the panel... sans approx. .5 -.75".
You're presently running a rear seat delete. If you move the inner wheelwells in more than the aforementioned .5 -.75", you'll never be able to re-install the original back seat without also narrowing the seat... and this is a royal PITA.
A couple weeks ago, I mocked up a set of 275/45/17's on the rear of the '66 FB I'm working on. The wheel was a 17x9.5 w/5.5"BS. To get them to fit, I'll need more BS. I had at least an inch of clearance between the outside of the tire and the inside of the fender lip, so I'm guessing (at this point) that a 6" BS would fit the 275's perfectly.
My wheelwells have been slightly enlarged, the rear-end has been narrowed and uni-body structural pieces have been replaced in favor of a full frame chassis, so don't compare mine as if it were stock.
Your dilemma is one that most novices overlook...
... the "overbuilt" engine is worthless in a car that can't transfer that power to the ground. You obviously took the time and spent the money to build the
engine. Now you'll have to spend a lot more to make that power useful.
I assume that you've tried all of the easier (cheaper) fixes? Traction devices, tire style, etc.?? When you have to stuff 315's, you'll need flares AND widened inner wheelwells.