Bump!
I started playing this game a bit yesterday and found a ceiling clip. It works exactly as you'd expect from a game that allows platforms near ceilings: just freeze an enemy near a ceiling, jump into it from directly below, and jump and while you're "oscillating" over the enemy. I'm guessing that if the jump is during the top frames of the oscillation, you'll go into the ceiling. Video:
https://www.youtube.com/watch?v=d3jhPdK9bfs
I haven't found any places where it can save time except for in the submarine. The TAS despawns the first ceiling enemy, but it could either kill an enemy along the way to make him spawn or just do the clip on the second enemy. It would still save time.
I have not found a way to move while within a wall. It seems to stop you pretty solidly once you're in there (until the enemy unfreezes). You can also jump above the screen during the 4-1 boss fight. You can't move left or right but you're stuck above the screen. You can still stab upwards or downwards into the boss chamber though!
http://imgur.com/ZpK7XVv,OUexa47
The only other interesting thing I found is that you can double jump after taking damage. Before you accelerate downwards like crazy, there is a small window where you can do a full jump in mid-air. I suspect the TAS could use this in the final fight to get hit by the bubbles and recover safely. IIRC, you take time to scroll bubbles offscreen before the very last hit. Perhaps this would help. It won't help in most other places because you can powerup your jump far beyond any need for a double jump, but it might be good for damage control after you get hit.
I'll update with anything else I find.