I had everything that moves down the screen under an "Every Tick". I just had to change that to "Every 0.016 seconds" to simulate the same speed at any refresh rate.
I would advise against doing that - very small times in 'Every X seconds' can still actually be framerate-dependent, as noted in the manual. For example if the game dips to 30 FPS on a slower machine, "Every 0.016 seconds" will actually be running every 0.033 seconds, and hence the game slows down in a framerate-dependent way. Also at higher framerates like 120 FPS, you'll have a janky appearance from moving things at a lower framerate than the game is actually rendering at.
The correct solution is, as before, to use dt. There is probably some movement happening in "Every tick" that isn't using dt and ought to be using it.