As I understand it, the 50-move rule must be invoked by one of the players, lets assume our immortal players agree not to invoke that rule.

The 75-move rule is automatic, so that would be the limiting factor.

Note, that 75-move rule is only applicable after no pawn has moved or a piece has been captured. So our immortals can do a lot of shuffling things around.

I'm thinking that the number of moves of the longest game is going to be (16 pawns * 7 moves each + 16 pawns being captured + 14 other pieces each being captured, not the kings) * 75 moves for shuffling around = 10650 moves.

That's only 1 week at 1 move per minute! But given the permutations, it might take much longer to calculate the actual moves required to get to the end state :)