MIT Mystery Hunt 2020/Toddler Tilt

Toddler Tilt is an interactive logic puzzle from the round of the 2020 MIT Mystery Hunt.

Puzzle Elements
Explicit Instructions - Due to "liability reasons", the rules to the puzzle are given explicitly:
 * 1) The puzzle operates on an 8x8 "platform" and four 2x8 "trenches", one on each side.
 * 2) Each move consists of "tilting" a single row of the platform left/right or a single column of the platform up/down.
 * 3) A tilt in a direction X moves the X-most letter in that row/column of the platform into the X-most open position in that row/column of the corresponding trench, then moves the other letters in that row/column of the platform X-wards as far as they can go without exiting the platform.
 * 4) The sequence of letters moved into the trench after each tilt is given.
 * 5) The platform state after tilts 10 and 19 are given.

Interactive - The puzzle itself is presented in interactive form, where the solver can click a button along the edge to simulate a tilt along that row/column. The applet also allows the solver to undo tilts and keeps track of which letter is the next to fall into the trench.

Typography - Part of the puzzle relies on the font containing letterforms with ambiguous orientations:


 * O can fall into any trough, as can SPACE.
 * S is two-fold rotationally symmetric.
 * The same letterform can represent E, M, or W depending on rotation.
 * The same letterform can represent C, N, or U depending on rotation.
 * While H doesn't appear in this puzzle, I and H would share a letterform and also have two-fold rotational symmetry.
 * The remaining letters (A, B, D, F, G, K, P, R, T, Y) have a unique orientation.

Deduction - Using these rules, you must deduce the final state of the Toddler Tilt Puzzle. This reveals...

Final Clue Phrase - ...four final clue phrases, which must all be answered...

Rebus - ...and then concatenated for the final answer.