I feel like the best way to balance the puzzles is to increase their importance. Alongside from being huge difficulty gates, they're also just genuinely really satisfying to solve. My biggest issue eith the diffculty, however, is *what* they gate. Unlocking the jobs is the best way to progress and that progress is halted the moment you get stumped. And the worst part is that is pretty much their only purpose.
I think that the puzzles are fun enough that they could be either their own game, or at least a bigger part of this one. They'd benefit from having mechanics from other parts of the game affect the puzzles.
My suggestion would be some kind of hint system, like powerups that hard lock pieces to certain parts of the board.
That aside, I hard agree. We need different voicelines.