Looking for new sway bar. Can I go too big??

Sway bars don’t improve traction?!
Uh, how do you think they improve body control? They add wheel rate, that’s how. And specifically where it’s needed during cornering. If you think that can’t improve traction, I’m not sure what to tell you.
Can you go too big with the sway bar? Sure. It really depends on your tires- if you don’t have enough grip for the effective wheel rate the large front bar gives you the car will understeer. Just the opposite with too much bar in the back, you get oversteer as autoXcuda said.
The trick is to match the wheel rates with the capabilities of your tires and the balance of your car. If AJ is still oversteering with 235’s, 1.03’s and a solid 1.125” bar in the front with 295’s in the back though I don’t think you have much to worry about. You’d be hard pressed to find a 17” tire up front with as little grip as the tires that are available in a 235/60/14, and if those 295’s aren’t more than balancing it out you can add a bunch more front bar before it’s an issue.
Also keep in mind not all of those bars are the same. The 1 1/4” Hellwig bar is a hollow bar, pretty sure the 1 1/8” bar is solid. The Hotchkis 1.5” diameter bar is hollow too, and without knowing the wall thickness it’s almost impossible to say what the rate actually is. All three of those bars could easily have very similar rates.

Hyup my Hellwig 1.125 is solid.My arms were tabbed.But the straight-armed bar is slightly too narrow so the links are not vertical. Doesn't seem to be a big deal.
My car was set up to run some soft-compound sticky 245-15s back in 2004 . F1s or something,I forget.I lowered the car, quite a bit at that time. It's a streeter and most of the roads are concrete. I set it up low enough that when pushed, it would settle on the bumpstops and wheel around the turns pretty good. But those tires burned off in a few weeks and because they were more than double the cost of the BFGs, and I was in a bind at the time (College for my eldest), I backed off the program for a few years. Instead,I raised the car up a bit to better use the front bar, installed some lightweight 7.5wheels I had with the 235s and found that cornering, while diminished,wasn't all that much worse. And in fact,while slower, it seemed to be more fun. Because the tires weren't saving myazz anymore, I actually had to learn to drive,go figure. By the time College was done, and daughter was self-supporting, I was several years older, and was quite enjoying the driving style I had come to adopt; so I just never went back to the F1s.
And you are right about the BFGs.They only work reasonably well for the first few thousand miles; then they get hard, and skate for the rest of their useful lives.After I learned to drive the skates,they're fairly predictable, and for me, it actually became more fun. I am talking all street tho. And I must admit, by 2012, I was coming 59, and slamming around turns too fast and skating thru them with careful power application, was not as important to me as it had been 10 years earlier.That chapter was drawing to a close.
You are also right about the 295s being a balancing act for the too-much front bar for the not sticky enough front tires, and the too-stiff shocks all 'round. On the street it seems I at least, could get away with crap. I mean go-carts have no suspension at all and those young kids seem to be having a whale of a time. I got just enough compliance so I can still see,lol, and most of that is in the air pressures. Works for me.
You are right about a lot of stuff.And when it comes to chassis work, you and AutoX are, IMO, top-tier.