Just came back from giving it a play and a rate!
I actually think the mouse controls have potential, they feel pretty decent. You could afford to tweak and juice them up a bit, but I don't think anyone is expecting perfection from platformer game-feel in a jam scenario.
I do think however that they aren't a good fit for the time loop mechanic.
Take this early level for instance:
I know what I want to do, but actually executing feels needlessly difficult with the less-precise mouse controls. I think you have to decide what your game is testing the player on; their puzzle solving skills, or their mechanical execution?
You certainly can test the player on both, but if you do you need to make sure that they don't get in the way of each other.
I found interacting with my past-selves required a high level of precision, which would have been fine in a traditionally controlled platformer where it would be easier to commit the actions required to muscle memory.
Both ideas are good, but not together! Like ice-cream and sausage, better apart.
With the mouse-movement idea, the controls will probably feel better if you have a visual metaphor that sells it. Like my character is something which chases the mouse cursor, or something similar. Something that makes the player accept that their control is going to be a little bit less direct.
If you're doing that though, I think you'd want to find some interesting ways to play with the idea that the mouse cursor and character are separate, but related. What if the mouse needs to activate a switch, but doing so will cause the character to walk in a dangerous direction? It could make an interesting puzzle platformer! There could be some great mechanical jokes you could pull actually, could potentially be very fun to design.
In summary:
- Mouse control is fine provided you're not asking me to do anything too hard.
- If you're using mouse control in future, be playful and explore the design opportunities afforded by having to think about the characters location relative to the mouse.