You could try putting the amp on the HTS850 by itself and connecting to the dedicated circuit, then run the hair dryer to see what happens. It wouldn't cost you anything but time.

My old house (roughly 1000 square feet, built in 1954) originally had only a 60A electrical service. When I set out to install a stacked washer/dryer a few months after I moved in (the existing dryer was in a closet on the back porch), I needed a new 208V outlet. There was no way to add the new circuit with the existing service, so I had it yanked down and a 200A service installed. If you've recently had an extra 20A circuit installed, I suspect that you are not in the same position that I was then, but you could ask the electrician who put it in what size the existing service is.