Because max moves replace your move slots, do they count towards being able to use last resort? Or would you have to use their normal counterparts to be able to use it?
Max Moves count towards the moves used for Last Resort. For example you can use 3 Max Moves and after the Pokémon reverted to its original form you can use Last Resort. You can also use for example 1 Max Moves and 2 normal moves and then use Last Resort too.
Source 1, 2.