Regarding the first suggestion: that sounds interesting, I’ll give it a try.
For the second one: you can “skip” the puzzle name screen by tapping on it (see https://twitter.com/mazzarolomatteo/status/12033866772359905...). Does it fill still slow this way? I haven’t added any “tip” about the tapping on these screens in the app... I thought this could have been discovered by tapping on it while waiting but I might have been too optimistic.
After playing more, and switching from a trial-and-error/backtrack approach to a more deliberate style where I try to mentally prove each extension of a line, I feel less of a need for the start-line-anywhere thing. So, it's your call on whether that's worthwhile.
It would be nice to have undo/redo--I've made a couple mistakes, and in those cases I'd like to step back and check my work move by move. That might spoil the clean design a bit though!
The tap-to-skip is a good trick, thanks--no need to make other changes there.