That sounds a bit harsh if a hand spring is allowed a higher start value, but there'd have to be a differentiation between kids who elevate higher than others.
As far as the practicality of moving mats etc........ Vault could be conducted in the same manner as the jumping events in track and field, which relies on coaches getting their jumpers over to the event as they wait for other events they're entered in. The mat set would start out at standard competition matting for a sufficient period of time for coaches to get those kids through the event. A "last call" would be announced to get stragglers over to vault before the matting gets changed for those wanting to compete timers, and increased in height as the event progresses to allow for hand front timers.
As far as the judges are concerned........
There're three things in that are certain in life. Death, taxes, and judges making mistakes like the rest of us. Judges getting thing's wrong, from time to time, is possibly the only reliable constant in the sport. They are, after all, human, and though it drives me crazy to see scores that conflict with performances, I have to admit that I've made mistakes too. So it doesn't matter to me whether they make their mistakes while my kids do handsprings *or* timers, because it is what it is and I'd rather spend my time coaching toward a destination beyond the handspring...... provided the kids are ready.