Originally Posted by Colnago Mixte

I train myself to instinctively only brake with the tire that still has air still in it.

I think to myself "right=rear" because in a moment of panic I can forget which is the front brake and which is the rear brake. Once I know whether it's a front or rear blowout, I proceed accordingly, and have always made it out alive, which you did too, congrats. I assume you're still alive if you're posting here, right?

Never had a simultaneous blowout on a steep hill, that really must suck.

Regarding the car, there's not a lot you can do.