This is the one case where tubular tires are far better. That same blowout would be a big heart rate spike, but slowing to a stop would have been easy. You can even use the front brake (gently). No big deal. BITD I did it at your speed and it was so uneventful that I don't remember when or where. (All assuming a good glue job but good glue jobs are easy to do.)
I'm still on clinchers but will be going back to the tubulars I rode 25 years because I want to go back to that secure feeling of knowing the metal of my rims is never seeing the road. (I blew a rear clincher going 25 MPH and did far worse than you - collarbone, ribs, acres of road rash and helmet slam. Bike did a lot better than yours however. A $500 "Team Dumpster".)