The only "reflex" my solution involves is at the very beginning.

Hmm. I wish there was an easy way to watch your solution. It might be entirely different than what I intended.

Just by looking at the map, I can reconstruct my route from memory:

Start with the obvious RDL, pushing red block L
Follow the block with another L, pushing it again. It will bounce off the red wall and come back toward you.
(the only timing-sensitive step the whole level) Just before the block gets back to crush you, duck out of the way with D. You'll go on a short trip to the yellow wall and back, and ideally in the time while you're out, the block settles onto the stop square. A slightly worse possibility is that you arrive while the block is settling into place, but that's okay--it just means another back and forth bounce before you finally push the block U.
Follow the block U and push it again, which will set it on course to land on the plate and open the red wall.
Now move R, then 3U to land on the lowered red wall and into the top section.

From here, LU will get you to push the yellow block and immediately bounce back. Once you get back, go U again to follow the block, albeit much further behind. This will take you and the block all the way to the leftmost square of the red wall, and push the block D.
Once you push the block into center ice, follow it D and R to put it on the plate, dropping the yellow wall. LUL from here now takes you to the wall.

Go 4U to the upper end of the yellow wall, L to push the block and bounce back, and L again to follow it. This pushes the blue block onto the same piece of floor that the "timing maneuver" took place on.
Don't follow the block after you push it past the wall: instead go 4U 2R 3U (plus the intervening ice tiles) to end up on the red wall, then 2L D pushing the blue block to its plate immediately. URD takes you to the blue wall after it drops.

2D takes you to the 1x2 connected floor, then 2R pushes the second red block around the loop so that it will end up on the left half of the 1x2, and you bounce back to the right half.
Once the block stops, push it L to fill the ice. Follow it to the new floor it creates.
Move D from the filled hole to take the longer half of the loop, so that the block arrives on the solid floor before you do nd you don't get crushed. You bounce back and automatically push the green block U, all the way to the blue wall.
Follow the block U, then U again to put it in the top square of the other 2x1 connected floor.
R 2L from here puts you on the yellow wall, then 3U to line yourself up with the green block, R to push, U to the red wall, and 3R D pushes the block onto the last plate and lowers the green wall.

Now just move 2R and spin around to the exit. At no point does this ever involve pushing a block off the right colored plate once it's there.

Ah, nice. I walked through your above solution to see what was going on. I actually screwed up in my level design a little and left an unintentional solution possible that you used. The level is supposed to require you to move blocks off of their colored pads at a few points.

If I update the level and upload it again, does it neatly replace the existing level or do something wacky like create a second level? I'd like to fix my level and reupload it without cluttering up the level list with old versions.