I'm afraid it just adjusts for the cycling speed of the current room so it can differ when you first enter it too. This game intentionally subverts many conventional game design principles, so it's fair that some people will find it throws them off. Some other ways it does this is how it's all designed around such a slow character surrounded by fast enemies (usually it's the other way around) and the timer system, as well as the bounce cancel mechanic (which you might or might not have noticed) when jumping on springs. That mechanic can even be used to adjust the timing of the mole when it sometimes seems impossible to get it right for the surroundings, but it's not required to master it to beat the game.
A password system is unlikely, but we are looking into using a save feature in a very discreet way (it will be in Slow Mole + if it all works out and feels right)
For now there's a cheat if you want to play the hard mode right away, hold select+B when going through the normal warp. Beating hard mode will take you to the 15 challenge levels (there's also a way to reach them on normal, but it requires meeting certain conditions)
That is actually a working cartridge prototype! But this version isn't gold plated, it's tin. But when we do a limited run of the updated version of this it's of course going to be gold plated. Here's a shot of the working prototype on a 1984 RGB modded Famicom: