Wow. Outstanding job on the history.

Couple of things...

I would recommend lowering the temperature on the "cool" side. You only have a 4 degree temperature gradient which doesn't give your snake an opportunity to cool down. The cool side should be around 78-80 ish.

The stain could be blood from feeding. Thawed rodents often ooze blood from their nose/mouth. Live prey sometimes bite the snake. It could also be some "waste" staining if your snake voided a little bit (they don't always drop huge loads). I wouldn't be too worried about it. Paper towels as substrate are great (I use them), but they do show everything.

Change the paper towels out, and you likely won't see anything for a while.

I wouldn't worry about constipation or obstruction. Ball Pythons are very variable in how often they stool, and if they are anywhere near shed, they will often hold it until just after shed. Your snake doesn't look the least bit distended.