I can report some improvement if the animation is on the Token or GM layer that makes these not looping animations at least usable with some effort. Most of this will not work on the Map layer.
I can now turn the looping on and off. (Also true on the Map layer but Play/Pause doesn't work there.)
If you have an animation that you want to start at it's beginning and run once and stop you can finagle it to work but it's tricky. You have to time turning off the looping the instance just before it restarts.
Once you get it reset, switch to another map and back or reload the page (which takes more time) and then you can run it again like normal. It will then run once and stop.
However, this is a one time shot. If you click the PlayPause button it will reset to start but if you click it again it will not run the animation but will skip to the end. But, if you reset it to start this way and and switch to another map and back or reload the page, you can run it again like normal.
Also, be aware that if you have two of the same animations. If you run the first one it will run normally but the second one will skip to the end. I have a workaround that works for my particular case (but may not help everyone).
My purchase came with static alternatives of the final states of the animations so I can place the static image on the Map layer under the Object layer animation and then delete the animation from the Object layer, switch maps and back and then run the second copy.
It's a pain but better than not being able to use the animations at all.
Last, be aware that two of the same animations on the map layer will loop in sync with each other as soon as you turn on looping.
Good luck.