I have been grinding away at refights trying to get decent RNG. I also had to go back and change the boss order in order to get good spider RNG.
After all of that I have finally made it by the refights with an actual improvement.
http://tasvideos.org/userfiles/info/59570921781781631
This is about one second improvement in game play over the existing movie. It's not much but an improvement is an improvement.
It's actually closer to 3 seconds of improvement, but I'm not counting using charged shots on the shuriken boss, which can be trivially patched into the original run.
I was about 5 seconds ahead going into the boss fights, but RNG has been destroying me. This is the best I could do after dozens of different paths and iterations through sigma 2 and the refights. No doubt someone can find a better RNG setup with enough time grinding it, but I'm happy just to make it to the end of the game at this point with real savings.