Robert,
I'm no expert, but when my pool is full (max full as you describe) my skimmer doesn't work at all. Or, at least it doesn't work to skim the surface (and thus bugs, etc. stay right on it). It needs to be at least 1/2 inch or more down in order for my skimmer to work.
For me (the non-expert) this makes sense, as the water needs to just come slightly over the top of the floating gate and when the water is too full there is no gate clearance (thus the water that is sucked into the skimmer is coming from underneath the surface). You can see this by swimming up to your skimmer and watching to see if the surface is clearing the opening.
So when we get rain and the skimmer isn't working I just drain the pool an inch or so and voila! -- suddenly the skimmer starts working again and the surface becomes remarkably clean. Like I said, I'm no expert so for the longest time I couldn't figure out why the top of the pool was so dirty (living in Florida we get so much rain at times the pool is always at max full unless I empty some manually). In about 30 minutes with the pool being lower I get a clean surface.
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