My frustration with wasting time (23 hours; I slept on it) on an unsolvable puzzle is somewhat mitigated by the fact the problem taught me this: if you count the free ends and come up with an odd number, you can know immediately that the puzzle isn't solvable, without rotating any tiles. An even number doesn't prove the puzzle is solvable, but an odd number definitely indicates a problem.
Edit: Nevermind; there was a 4th loose end I was overlooking. Finding it led to getting unstuck & the puzzle was solvable after all.
Unfortunately due to the way the site works, I don't seem to be able to get a new 10x10 puzzle by refreshing the page? So I'm stuck on the unsolvable one. I can imagine saving the progress is a feature, but you should also add a "pass" or "skip" button. Oh - I just realized I can "hack" it by manually changing the number in the URL to something else, e.g. /10/851.
Before I realized the puzzle was unsolvable I was also looking for a button to randomize/reset the initial tile positions. I was thinking maybe I wasn't seeing the solution due to my preconceived ideas from already-placed tiles. That wouldn't have helped here, but maybe on a solvable one being able to re-randomize would help a player get unstuck.