Sorry for the delay in reply, I just got through a massive house move!
This is the best kind of comment, from a true Alex Kidd fan. Thank you for pointing out the differences, those are things I missed. I like to think if this is the list of differences, then I must have come pretty close! Sorry about the missing 1-ups, my only logic was that the ? blocks had a ring in them, unless you already had the ring, in which case it's a ghost. That's the only behaviour I noticed in the original, so that's how they all behave. Not sure why the merman has mercy invincibility, maybe it uses the same code as Alex Kidd - it was a while ago and I had to cut a lot of corners to get all the code to fit in Pico 8's memory limitations! Also same with the Ox boss, he re-uses some enemy behaviours because there is literally zero bytes of code left! It can be done though, I have playthrough I recorded in a single take up on YouTube.
(I understand of course, that as the developer, I'm more used to playing it than a new player.)But as for the Janken games, there is a trick - it's time based. If you watch closely to the changes they make, you have like half a second to react and change your option to beat theirs before the time is actually up. I figured this was more of a challenge than them all having the same pattern every time, though maybe I should be more up front about this change in the instructions. It does get a mention though.
I'm glad you're willing to keep trying :)