A friend of mine is doing a Mosin conversion with a wildcat called ".458x54R." It uses a 7.62x54R case opened up to take a .458 bullet.
The 54R case is .018" smaller in than the .45-70 at the base. He plans to wrap a thin piece of tape around the base to keep it centered for the first firing, so the case will blow out centered. I used to have to do that to .303 brass, with even more chamber clearance than that in a very loose SMLE chamber.
After that, he plans to neck size with a .45-70 die.
The 54R case is .010" longer than the .45-70 in its necked form; a bit shorter when opened up. Not a big issue for a straight cartridge; it should run fine in a standard .45-70 chamber.
Bob plans to use the skeletonized magazine trick that Willie pioneered with his .45-70 build, but by using 54R brass, he doesn't have to do any bolt mods at all, so his conversion consists just of the barrel and magazine mods.
There have been a number of proposals for other cases for a .45-70 variant, to avoid the hassle of the big .45-70 rim. Some people have machined the rims down to a more manageable size. But the .458x54R ought to feed nicely through any Saiga .410 mag, and the 54R rim can be accomodated in the AK bolt face, as demonstrated by the PSL and some Russian-market Saigas.