Those pesky defrost drains do get clogged up at times. If you only removed the plastic, you may not have gotten it completely de-clogged. I use a turkey baster and hot water to flush that sucka out. Works everytime!

Hope that helps!
Rodge @ Flipping Appliances On a Shoestring Budget

Check the freezer temperature.
It should be between 0 and 5 degrees F.
Could be it is too cold so the water freezes before it can drain.

Check that the drain tray is nice and clean.
Also sometimes a buffed up coating of wax will help the water to drain faster.

If all else fails get a length of 10 or 12 guage wire wrap it a couple times around the defrost element and then down the drain an inch or two.
\Wrap ity snug but not super tight.
Also a good idea to force a defrost cycle to check that it does not get too hot.

Below is a more elegant part that does the same thing.
Click on the picture to get more info on it.
Part number: AP3119957

In the end there should be a reason why this is happening...
Yes there should but I do not know what the reason is.

I can tell you that the symptoms and time line you refer to is basically the same as others who have posted but I have never seen a post that said they found the cause.

Either of the causes you give could cause the problem.

There is also a possibility that the freezer is getting too warm occasionally and water is dripping down onto the pan.
To check for this put a bowl of ice cubes in the freezer.
Leave them here a couple days then if they are all frozen together you know the freezer got too warm.

Also it is possible that a piece of foam etc. by the evaporator coil has come loose and fallen etc. so that the air flow in that area has changed.