We also have survived several high speed front flats without going down.
Don't panic. Do not grab a handful of brakes!
Always been able to ride it out although a couple of them felt like were riding a bronco in a rodeo.
Stay loose on the bike and don't tighten up hold on the handlebars.
Also done a couple spectaural rear flats . . . like when tire we were test riding blew off the rim and it wrapped tbe innerube into the freewheel . . . instant stop (again!) and showering the guy that was drafting us with pieces of flying rubbe.
However, most things we worry about never happen . . .