I was able to spend some time looking at it tonight and here's what I learned (and a few things that didn't help)
First off, I attached a few pictures of the card to this reply.
My first thought was that perhaps it was a heat related issue, so I added some heatsinks to the 3 main chips. That definitely cooled them down some, but unfortunately didn't solve the "red static" problem. Probably not a bad idea for longevity though if I can get this fixed.
I found that if I touch the card in a specific spot right behind the second TMU, the "red static" problem gets worse. Strangely, its nowhere near the output side of the card.
https://imgur.com/a/8GHRNR3
I also noticed that the board had a bit of a bend in it, so I thought perhaps there were some questionable solder joints in that area, so I reflowed both TMUs and the frame buffer chip. I heard them "adjust" shall we say when I reflowed them, but no change. I then hand-reflowed the bypass caps and resistors behind the TMU, right where touching makes the difference, but still no change. I then touched the board in the same spot (physically), but through an electrically insulated material (digikey bag 🤣), and it didn't have the same effect. So it seems that the act of physically touching it with skin that seems like it is causing some kind of interference, like interference being capacitively coupled into the circuit. I took off a few of the 10uF SMD capacitors on the board to check them with my ESR meter and those checked out okay, so it doesn't seem to be bad caps.
Touching anywhere else on the board doesn't seem to have that effect, just that one particular spot