Thanks for the reply!
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.