Just bought this (it's 50% off for Black Friday) and documented some possibly speedrun-related info about it alongside Jim in a video call.

Gunslinger is its own category but its rules don't go into detail about what other settings are allowed or disallowed.

In addition to Gunslinger mode there's Mega Life mode which doubles your life - pretty insignificant for a speedrun - but there's an unlockable Mega Shot mode which doubles the damage of your weapons but not melee. This changes strategies significantly as a couple of bosses or enemies that are quick killed with melee or dash attacks are now faster with certain weapons.

There are built in save states, which work as expected. After finishing the game you're given the option to save the run as a replay. It only includes the footage after your last state load. It doesn't seem to be a video file; AFAIK it's an input movie kind of like you'd see in a TAS. It properly recreates any lag the original playthrough had, the same patterns and RNG, and even pauses the game as you did.

So my questions:

Is Mega Shot mode allowed?

Is submitting a replay allowed? The only reason I ask this one is because of how difficult it is to capture video off a 3DS, and timing + submitting from the replay feature would make it easier. Because the replay starts rerecording after a load state, it's not possible to save state scum a run to optimize play, dice rolls, boss patterns, etc. without it being clear through the replay function, since it would be an incomplete replay.