It might also be useful to include certain other things in the search list, such as names of layers and brush presets to quickly find and activate one

This seems like a very useful addition. However, there's a couple of problems with this approach that need to be addressed.

Setting the timer precise does not seem to be necessary. I also fixed returning to the correct frame when stopping playback.

Simplified frame dropping logic

Fix erratic jumps into middle of the playback range when reaching the end

Nice work.

Fix delays after adjusting FPS during playback

Remove an extraneous rounding.

Changed to using frames as the fundamental unit instead of two different types of milliseconds. The logic is now hopefully clearer and more correct.

Re-upload of the diff. Previous patch file apparently did not include all the intended changes.

Fixed a time-origin mismatch between using a timer vs. audio playback for timing. After this change I can no longer reproduce the regression.

Fixed the issues Dmitry found.