The .44 AutoMag started out as a much shortened .308. Cut to 1.298", remove 3 thou off the rim diameter and ream the case mouth to .428", .590" deep. Same body diameter at the head as either the .308 or .30-06. Too short for an M305 action without major modifications.
I'd bet it'd work through an SKS action without too much work though. Only 226 thou difference in case length. Only 25 thou difference in rim diameter. The 7.62 being smaller.
Cu$tom barrel$, either way.
There is/was a .44 wildcat that is literally a .308 without the neck. Can't remember what it's called though. Most likely more than one too. You're not the first to think about it.
"...Rimless cartridge needs a shoulder to head space on..." Nope. Headspace on the case mouth like a pistol cartridge.
"...it's already been done...." Of course, it's been done. Everything has been done by some guy, somewhere, at some time. Not likely in an M305 though. The cost of a custom barrel will kill it anyway. Doesn't mean and shouldn't mean one should stop thinking.