> And you can derive an easy upper bound from that as 50x8x8x2 (basically each 50 moves you make a pawn move)

This is not high enough, because the 50 move rule also resets when a piece is captured.

Actually no. 50×(16×6 + 32) = 50×(16× 8) works I think. Every 50 moves, move a pawn or capture. There are 16 pawns. Each pawn can be moved 6 times, so there are 16×6 pawn moves available. In addition there are 32 captures available.