A simple proposal, a four/five issue miniseries (like warriors of mars, white apes of mars, or fall of barsoom) that explores john carters immortality
it would be a period piece, probably taking place sometime during the roman empire, or perhaps sometime earlier or later. It would show John Carter as the man we know in a time of ancient earth, doing what he does best!
it would also be an excellent comic for exploring the connectivity of burroughs worlds. Perhaps showing the effects of barsoomian technology somehow making its way to earth, or showing some of the more fantastic creatures of earth created by burroughs!
Personally, I would have John Carter as a warlord of a small group trying to leave the roman empire, a man fighting for the freedom of these people .. . . it would be early in john carters life, and he wouldnt exactly be the same man . . . once or twice I would show him changing a prayer to mars the god of war, or perhaps those he fights for thinking he is mars . . . yeah I would go overboard with the mars stuff
there would be some fantastic beasts of course controlled by a "sorceror" these beasts would be dinosaurs and other creatures ripped from tarturus . . . or did romans use the term hades? Still, dinosaurs ripped from pellucidar to give John Carter something cool to stab!
A quick and violent look at john carters past, fun fast action!