info so far

There are 2 RNG seeds that I've found so far that the game uses
what I'll call "RNG1" is an array of 4 byte (int) seeds that is 624 entries long starting at 0x816B2C54
0x816B2C50 is the index of the current seed

RNG1 is what causes the gold hands to spawn
RNG1 doesn't seem to get called for a whole lot of things
so the hand manips make sense here, rare calls + consistent starting seed = consistent starting results

what I'll call "RNG2" is an array of 8 bytes (long) seeds that is 15 entries long starting at 0x81B9B200
the game keeps 4 pointers to these seeds
0x816E9D78 - points to the start of the array (always 0x81B9B200)
0x816E9D7C - points to the 4 higher bytes of the current seed in the array (changes)
0x816E9D80 - points to the 4 lower bytes of the current seed in the array (changes)
0x816E9D84 - points to the end of the array (always 0x81B9B278)

RNG2 determines what battle you actually get from the shadow as well as other things
RNG2 gets called a whole lot, it seems to be tied to particles and most other random stuff
a few example calls that might be relevant:
    The falling star animation on the title screen (spawn position, speed, size)
    The TV animation in the corner of the loading screen (color pattern, teddie animation)
    The position of the midnight channel in the TV listings (main menu between midnight and 1 am has an extra rng2 call)
    Particle effects (the full screen filter effect while in the TV world might call this)
    In battle RNG calls (damage, hit, crits, ect)

Both values are seeded at the start of the game using the same value (0x9A319039)

the fight you get seems to be seeded when you enter the floor
mashing x to get past the title screen to load seems to get consistent seeds (the midnight channel does add 1 extra rng2 call)
RNG2 doesn't get called on the load save file menu
RNG2 seems to be called pretty often while standing still (probably for Yu's idle animation)
RNG2 still gets called occasionally when moving though (probably by something else, a ui element maybe?)
You can use the stars/audio on the title screen for a cue for whatever seed you want
With buffered movement and mashing entering the dungeon should give you the same seed
You can use the color of the TV animation on the loading screens to verify your seed
Physical seems to have variance in loading times, which does end up mattering. So digital might be the way to go