Battery relocation for HANDLING (not drag) - best spot to mount?

you can get sticky 15's :D
EAGLES, PIRELLIS, KOOKS and TOYOS ONE, TWO, THREE, FOUR.

Except almost of those also have a sub-200 treadwear. Which may be street legal in some cases, but they're not really streetable tires. The Toyo R1R, the only one with a 200 treadwear, has it's widest 15" option as a 225/45/15, which is only 23" tall. And is still narrow for handing.

Even for an AutoX car the sub-200 treadwear can be an issue, because a lot of classes that you would AutoX one of these cars in require 200 treadwear or higher (CamT for example). Sub-200 treadwear tires put you in really competitive classes.

it’s a small change moving to different location and getting measurable results (track times) and data acquisition.

It’s one of those little things that’s known by physics and engineering. You do a bunch of little things and it adds up. But individually might be tough to measure (especially home build)

There’s a few things happening:
-one is the inertia effect of the car swinging or yawing around its center or gravity (top view)
-another is the weight transfer from center of gravity height (side views)
-another is tire loading weight balance on scales of (top view) *this tends to be the most significant and measurable change.

Exactly. If you want to locate the battery perfectly for handling, a set of corner scales would be the way to do it.

Short of that, all of these cars are nose heavy unless you've done some really serious weight management. Even then, probably still nose heavy. So if the best handling you can get is the goal, you want a front/rear weight distribution as close to 50/50 as you can get it. Which means putting the battery in the trunk. Where exactly you put it in the trunk would be a job for the corner scales again. But my general inclination would still be the passenger side for most of these cars.

This is Tomswheels Valiant, which had a cage, the battery relocated to the trunk on the passenger side behind the wheel tub, fuel tank in the usual location, WITHOUT the driver. Small block car as well.
weights copy.jpg

On this it shows the passenger rear as heavy, but, with the driver in the car that would definitely change. And the car is still nose heavy. This is just one example, not every A-body would match this, but as a general idea I would still suspect the trunk on the passenger side would be the best option for most cars. That's where mine is, but, I did that without scales or anything so it's no more scientific than what I just said.