"Jim2009" ...
When it leaks open the door and inspect the water level, it if looks high
then you have a problem with the float shut-off.

How can I tell if it looks too high? I like this idea of analysis, yet I do
not really know what to look for...

Another off-the-wall idea ....inspect the hinges and the latch for
loose/worn mounts.

Good thought, the door seems to be not loose at all and clamps seemingly
tight.
Tomes