So TheC64 issue looks like it's running in NTSC mode. Given the speed of the music and snow falling, it definitely looks just a few percent faster even though you've set to PAL mode as you say. There is a bug in the firmware I believe. What you need to do is factory reset TheC64, reboot and then select 50Hz and save the settings. Then re-run the game. I've read that switching between PAL and NTSC via the menus doesn't save the change unfortunately. It will affect all PAL game, not just my game.
As for the RESTORE key issue - it looks like you already had an issue before pressing it, as the title music was still playing in the level with the timer paused. I will look further into it as I've got an Ultimate64e, so should be able to recreate if it's U64e related or not. I've also asked one of my playtesters to see if they can recreate the issue as they also have a U64e.
Thanks for the feedback and videos. Very helpful.