The longest tournament possible is one which a) takes the longest time possible per round, and b) has the most rounds per player.
Byo-Yomi is best for maximising time per round (yes, I know I spelled that wrong, but I can’t be bothered to correct it!). It is better than Absolute because (duh! I shouldn’t have to explain this, but it’s main time is equal to the Absolute timing’s maximum time). It is better than Simple because it is basically simple but with more periods. It is better than Fischer, because, when pushed to the limit, Fischer is equal to Simple plus Absolute. However, Byo-Yomi is Simple * 300 (I code, so I like *, instead of x) + Absolute, which is better than Fischer. Canadian, when pushed to it’s limits, is basically a worse version of Fischer. Also, you should use a 19x19 board.
To maximise (spelled it wrong again! :)) tournament rounds, Double Elimination is best, for it gives (optimally) log 2 of player number * 2 rounds. However, it is only better than McMahon for 64 or more rounds, as for less than 64, log 2 64 or less times 2 is less than 12 rounds, which is the round number you can have for any number of players.
(BTW, if you exclude superko, the game can go on forever! Including superko, the lower bound is 10^48 (10^170 board positions, but not all can be cycled through! https://senseis.xmp.net/?NumberOfPossibleGoGames))