Recorded on Snes9x 1.52. So far, this is an improvement of 1295 frames over Fladdermus' movie (I know it's not a completely accurate comparison, seeing as how his run was done on Snes9x 1.43). No clue if I'll be able to see this to the end, though...
Anyway, waiting to equip the Short Sword at the same time as the Power Ring (needed to bypass the slimes at low levels) saved something like 1/4 of a second, due to pulling up the equipment screen only once. It would've been a little more time saved, except I had to sacrifice some frames to jump over the enemies (particularly the first ones) prior to that, instead of slashing right through them (unless traversing slopes, jumping wastes 2 frames vs. normal walking).
Bosses went pretty well so far, although I was unable to alter Dulan's pattern whatsoever (Fladdermus' movie had him at the same position the whole fight), but at least it left me pretty close to the Long Sword. The gargoyle I was able to sneak in some more hits by doing otherwise unnecessary sword thrusts after landing a hit (I don't know why, but if I didn't do those, I often wasn't able to land a hit during my next jump - at least they don't waste any time).