Thanks to everyone for the posts and suggestions.
My responses, in no particular order:
Regarding the screws and possible leaks - When I removed the doors and frames late last year, I sealed everything inside the frames before replacing, as well as caulking every screw hole before re-screwing. Having said that, I don't think the screw holes are the problem because the screws are located outside the frame area where the gasket is located and below the wet area. I checked the interior against the wall and could not find any moisture that would suggest water is getting in from the screw holes and wicking up to the carpet.
The door itself is a good thought. When I checked, there did not seem to be any moisture on the inside of the door. And the door itself has two holes along the bottom that allows any moisture to run down inside the door (should any water get inside the door) and exit into the area where the gasket is located (which is outside of the flange area previously described). If the gasket is doing it's job, it should prevent water from getting past it into the interior. I will be taking a closer look and consider sealing the door as well (where the door and it's frame meet).
Funny enough, one of my first thoughts was to lock myself in the compartment and have someone pour water on the outside. Will likely do that after I reseal/re-caulk if it needs it.
If trapping myself in the compartment does not work, I may consider the pressurize test.
And last, if it does turn out to be the wicking issue that TVOV describes, I'm not sure what I will do. I can't just caulk the **** out of it because, as you note, the door has to open and close.
My next move will be to replace the almost brand new gasket with another size/style to see if that works.
Barring that, after all the issues this thing has had, I may just wait until the fourth of July and blow the thing up in a great big spectacular celebration (smiley face should go here). I will be selling tickets to cover the cost of the dynamite. But refreshments and a lawn chair will be included in the price.
Marv