Thank you for your feedback!
I actually had more action based speedrunning game concept about the game but then I went with puzzles in the end because that's easier for me to design.
About jumping and collisions: there has been also other comments so I have now fixed most jumping related issues that with some help from Vendolis. The problem that you had with platforms moving differently during different attempts is also a known bug but it happens relatively infrequently that it is really difficult to debug. My best guess so far is that it would be related to frame rate inconsistencies.
Your last point is also something that has been repeated by others too. Rewind mechanic is interesting solution idea but I fear that it does not fit the narrative or theme. Maybe if I would just change the theme to time travelling that could really work as a mechanic. I will have to remember this suggestion. Maybe I will make a speedrunning time travel game somewhere in the future.