You’re right, wrt potential sources of errors.
FYI - I estimated the tire groove reduction at 1½” (~27% reduction of Patch) and it truly was an estimate. Also I have an analog tire gauge which is not the most accurate.
Here are some impacts of source error that you mentioned that I came up with from my calculation:
Air Pressure: ±1 PSI – impacts output by ±2% error
Groove Est. or Patch measurements: ±¼” – impacts output by ±4% error
I think the patch method is a valid way to obtain weight estimates at home, but I’m still a strong advocate for going to a scale to get accurate weights of TV and TT. If you’re interested here’s a link to when I posted my tow vehicle and trailer weights and how I measured them at a scale