I guess I could use the term "cylindrical bullet", its more accurate.

The round ball will shoot through deer reliably to 150 yards or so considering 50 cal or larger and broadside shots. Based on actual deer shooting and testing penetration using baffle boards.
A friend shot through a doe from side to side at 120 yards with a 45 cal RB last year.
Can I shoot one in the butt going away and hope for a clean kill? I suppose the 16 bore will with a WW ball would do this shot if I were tempted to try it. I would pass on it with a 50-54.

Penetration must be ADEQUATE. It need not be excessive. But the idea that a 260 grain cylindrical bullet is too light for deer is simply silly. A bullet that blows up on a deer's shoulder is USELESS totally USELESS. Why people would even use such a thing is beyond my comprehension.
A pure lead 255 from a BP loaded 45 Colt revolver will kill deer very well with decent shot placement, but the velocity provides "adequate penetration".
The same with 45-50 or larger caliber RBs.
A round ball of 260 gr driven by 30-40% of the ball weight of blackpowder will kill any deer or elk shot with the shot placement (shoulder) that caused the bullet blow up that started this discussion. At least to 100 yards on elk and likely much farther, probably 200 for lung shots. (If Parkman's guide in "The Oregon Trail" could kill 2 buffalo in 2 shots at 175 yards penetration with a 50-54 will not be an issue with deer at that range.)
Even if the 260 gr RB strikes the shoulder bone on a deer at the distance the deer was shot by the bullet it will GO THROUGH it and kill the deer. Likely at much longer distances but I lack data since I almost always do lung shots.
Apparently the 260 gr bullet will not.
If the rifle will not shoot RBs then you apparently bought the wrong gun or it needs more load development. If it has a 48" twist it should shoot 90 gr of powder unless its rifled too shallow. I had a 48 twist 50 with RB rifling that would shoot into 1" at 100 for 3 or 5 shots if I did my part, 90 gr of FFFG and loaded with just the rod, no starter. But my eyes were a lot better then.

Dan