As it happens, we've been looking at GPS as a means of determining position during a sequence, but from a judging perspective - but using civilian kit on a reasonable budget, still doesn't seem to be a reliable mechanism when it comes to Advanced/Unlimited sequences.
Well, about half of those sequences are flown inverted so you would need a GPS antenna on the belly, and a GPS who can receive input from two (or more) antennae. Also the sample rate of one second may not be enough for the more snappy maneuvers. And your average GPS will not have gyros internally so determining the exact attitude of the aircraft for ZLA purposes would be impossible.
Combine this with the fact that you'll probably want a standalone (non-panel mounted), security-sealed unit, it'll probably be a long shot. Nice idea though.