I became impatient and applied latex paint to a cabinet door way too thickly. I dumped about four ounces on the door with the door laying flat and then just spread it around with a brush. Will the latex dry thoroughly but just take longer or did I mess this up?
Yes it will dry and it will "dry" in a couple days with right temp and air flow controls.
However with the amount that you put on there it could be a long time before the paint actually cures and it may never cure to the point of a good paint job. Depending on a lot of variables even after it cures the inner paint may become rubbery or even worse it could become chalky and never bind right.
It will make it easy to strip off and redo correctly. It should peel off like plastic when it's dry. My home had very heavy latex paint on cabinets, and I was able to peel it all off with minimal scraping.
Cabinet doors should really be painted with spray enamel. It will look 10 times better and last 10 times longer than latex.