There's a trivial way to beat the Test of Speed that I haven't seen mentioned anywhere else: do the entire thing in combat mode. The fire will only move forward once for every 8-16 steps you take, rather than once for every 1-2.
Everywhere else recommends having someone with boots/potions of speed, who can take out multiple enemies per turn and has piercing crystal, but I was able to grab all the goodies and beat it easily with none of those things.