Bullet style depends upon your intended use. For hunting, a jacketed bullet would be OK, try for size in the chamber (or cartridge case checking die). CAS, SASS shooting allows lead bullets only. If hunting is the goal, watch the pressure in a toggle link rifle, the loading manuals differentiate the 73 with a lighter maximum load than the 92 or the Marlin.
The thickness difference is only a thousanths or so, just that Winchester happens to be the thinnest (in that caliber) and allows a 428 or 429 to chamber in most cases. The chamber seems to be the limiting factor here, as many revolvers have cylinders that won't accept a 429 bullet, but have a 429 bore. I have Colts and an Uberti or two that needed a finishing reamer turned in them to even accept 427 bullets...
As far as the thicker wall adding strength, not enough to matter as far as making for a less delicate case. 44-40 brass is half the thickness of 44 Magnum.
As for cleaning a leaded barrel, I've never had a problem. I use both Moly coated and regular lubed lead bullets, none have ever leaded beyond what a Lewis Lead Remover can't handle, and that's after several months of CAS matches. Usially, a cloth patch will clean it.
The rifle doesn't lead as badly at the chamber end of the bore as a revolver does, probably because there's no cylinder gap, or difference in cylinder throat to bore diameter to overheat the base of the bullet.