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35 Remington is what you seek......
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This guy ^^^^^^ gets it OP. If I were in your situation, I'd go 35 Rem in a second. You can use 357 cal pistol bullets from 110 grain to 200 grain, and there is factory ammo from 150gr-220gr out there. It is a handloaders dream as well.
IIRC there is a "One Load" using 13 grains of Unique (or something similar) and a lead round ball that is a pussycat for plinking and small game.
Am I correct in that you said there are minimum diameter limits in your state? If yes, no change in my answer.
If you can go to a smaller diameter, I would build one in 7mm TCU. 120-150 grain bullets around 2100 fps will kill 75 yards deer all day long.
ETA: Boudreaux and Bubba's bait and Boudin Emporium are FAR, FAR more likely to have the 35 Remington ammo on their shelves than the 357 MAX or 350 LEGEND, just saying. Matters if your not a reloader.