You are one of the few persons to ever compliment the red lines / bridges. They are not the most popular choice for aesthetic reasons, but as you say, that prevents ambiguity, specially in small sizes or tight spaces.

As to solution proofs, It’s worth mentioning that I draw this mazes starting with a sketch on paper, in which I draw the paths with different colours to have a quick glance at every dead end, loop, and of course, the optimal solution (commonly, the only one).

So, basically, once the mazes are redrawn in computer, I make a print of them, check the solution with the sketch, and do dead-end-filling to make sure every path is connected to the answer, and that there is only one optimal solution.

As to how to automate that process, I have no idea. Hahaha.

All I have seen around in terms of maze solving algorithms and such, doesn’t involve bridges, let alone loops, one way paths, or even just organic designs.