I've routinely seen estimates at 1-2 PSI per 10(f) degree change (depending on tire) and 50+(f) degrees of warming over the first 30 minutes of driving at highw

I've routinely seen estimates at 1-2 PSI per 10(f) degree change (depending on tire) and 50+(f) degrees of warming over the first 30 minutes of driving at highway speeds. That's a change of between 12.5% and 33% depending on tire. Additional load doesn't change the total volume much - so it's not directly increasing pressure - but it can increase deformation (as you pointed out - contact patch size changes) creating more warming, which will increase pressure.