I assumed whatever inherent issue was causing crashes in the browser build would be fixed by halving the size of the maze.

I was wrong.

After running Unity's memory profiler thingamajig which I hardly understand, I think I did actually find the problem this time.

The one thing which kept getting bigger as the game went on, 
and so ate up more memory, is the combat log. I never, at any point, cleared that text field and it would grow to hundreds if not thousands of lines long over the course of playing the game.

So now it removes lines once the length goes over 100 long, which should fix everything! Right?

I also uploaded new versions of the Windows, Linux and Mac builds since they did share this problem and were also draining memory unnecessarily.