How much improvement will I see?

I would go with a convertor that stalls around 4500. That combination ultimately should be able to threaten the 11’s.
I had a stock short block 360 in my current car when I got it. Initially untouched eddy heads( so yours should be better) 750, airgap( I would ditch your single plane) 4.30 gears, and Hoosier bias quick time pro 28 by 10 tires. Low 240’s at 50 comp solid
Car ran 12.23 very first time I ever had it out at 108-109.
If you are truly wanting to step the car up, I would do those 3 things, more camshaft, more convertor, and swap to a good dual plane like an air gap.
You won’t have any issues hooking what you have with a good 28 by 10 tire( like a Hoosier)
You should be capable of making 450 horse with a few tweaks
This is the cam I recommended to my buddy who bought the 360 I used to have, and he has it installed. I had pitched that junk comp cam and switched to a bigger Howard’s that I still run in my stroker.
This cam, assuming those heads are half way decent, the dual plane and a real convertor, as I said should seriously threaten the 11’s and be fun on the street to drive. And yes, that cam would be plenty street friendly, just don’t wimp out on a convertor you will never be happy with. Get a tight 8 inch that will flash around 4500, and hang on.

Mechanical Flat Tappet Camshaft & Lifter Kit; 1964 - 2003 Chrysler 273, 340, 360 3000 to 6600 Howards Cams CL711262-08DL | Howards Cams