'67-'69 Barracuda rear tire size

The biggest tires that will fit in there are 325/50-15. A little massaging if the inner wells is required;very minor. You will have to move the springs inboard with the offset hanger kit.With a lowered car,it will occasionally rub. To run a 4.5 bs the housing/axles will need to be narrowed.
For no wheellwell mods ,but still using the narrowed rear,295s will fit. No cornering issues at all.
With the standard rear, 295s will fit with a larger bs.
With the standard rear, 275s will fit on 4.5bs

295s and up need 10inch rims, for reasonable tire life.
275s need 8s

295s do pretty well behind a 360, for at least 2 summers with moderate driving.Then the tire goes hard, and the grip goes away.
275s do pretty well behind a 318-4bbl;perhaps several years.But a strong360 can run the soft part off in a summer with almost normal driving.After that they can last several years, but the grip is gone.
255s will not survive long behind a 360, with any aggressive driving.
245s can be burned off in no time.I would only put them behind a slanty.

This has been my experience.

EDIT
For 295s and up, on 15X10s and a 4.5bs,You will need a narrowed rear.
I don't recall how much I cut out. But I do remember that it can't be any narrower and still put the springs on perpendicular to the ground-plain,with the offset hanger kit.There was just enough room to install the U-bolts, and then the bearing house was right there.Oh, and mine's a 68