Ok, so I solved one maze from 1993. It was a maze from a competition known to make hard mazes. I created another maze from a 2004 competition. It solved the maze. It back solved by a different route. It did its speed run on a totally new route and got stuck. I'm just starting to work this out. Here is the maze if you want to try it out:
Example Maze 2
On the other hand, it does solve this maze from 2002 that I recreated. It looks like I run into problems on two fronts. First, if the first run and back solve don't reveal enough of the maze. Second, if a run hits an unexplored region and the only open spaces available have cell values greater than the current cell. I need to solve the "stuck" problem for sure. I will also want to add more "exploration" to the back solve phase.
Here is the other maze I was able to solve successfully ( if not optimally; I haven't checked ):
Example Maze 3
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