Exodus

You nailed it! Okay, I had no idea about the 5/5 TID/SID. I ran it through aaaaand: 19832 xor 19832 = 0 So, yup. I just generated a bunch more shiny charmanders with random PIDs, and one of them is ultra. Ran the numbers through and it also = 0 Well done!

Do check my edit above, though. I re-edited my three charmanders to try to make them all Ultra, then none were after that edit. So, whatever happened with my Lucario and (the first time I edited) Charmander, I dumbassed-lucked into it. There's something else, and Charismatic Mark may have nothing to do with it (my Lucario just happened to have it, and he's ultra). As difficult as it is for me to believe the chances, the Charmander must have had "it" to the first time. I rerolled the PID and encryption constants when I re-edited him, so your maths may very well be the cause. But my Lucario didn't meet your requirements laid out when I did the Xor calculations. Hm.

Sorry, editing this due to one simple thing: it did not work on my third try. As difficult as it is to believe I stumbled with blind luck into it, altering my charmander again and reloading it did not produce ultra square sparkles this time. I still have my ultra shiny Lucario, and I won't edit him again (so if I need to test some maths against his values or whatnot) so am happy to help use that to figure out what it may be. Very, very odd...

That seems like a lot of math. I made my Lucario an Ultra Shiny (square sparkles) by making it shiny and giving it the "Charismatic Mark" ribbon. Edit: (I'll note that I did the calculations above, as outlined, to see if I just happened to luck into something, but it ended up being 765600 xor 19832 = 779224, so wasn't even close.)