After about a dozen tests, and much discussion, the discord and I managed to find the actual requirements to summon Umi! Thanks to everybody who contributed theories, and special shout-outs to CrypticDX, who was also in the lab trying to figure this out.

Umi is summoned by leaving a black hole pick-up on the ground, in an area with a modifier, for 4 mortality levels, at which you will hear a quiet jingle, indicating that she spawned. Her approach can be interrupted by a boss spawn, but this doesn't get rid of her, as she will be back after the fight. She will then begin to approach the black hole. Right as she is about to pick it up, grab it, and trigger the fight.

IMPORTANT: at the time of writing, statues mess up the timer for her spawn, either un-equip the statue skill, or get rid of the one in the current area asap. I'll go over how to best do this in the next section.

The process I've dubbed "The Ritual" is the most consistent way I've been able to summon her, and it's worked everytime. This also garuntees consistent timing, and no interruptions.

First, equip spaghettification. This spawns a black hole pick-up upon defeating a boss. Pick-up every other item. (not required, but makes things easier) Then, seleft an area with a modification. Which one you pick depends on the statue, if you have them enabled. The statue should be one that leaves after activation, I.E. Statue of Protection, or Statue of Relief. This makes sure she spawns before the boss shows up. If none are available, you have to rely on chain-grenades in-order to get rid of it. If done correctly, her jingle should play at exactly one mortality before the boss spawn.