It turns out that the Windex wasn't enough to keep the keys clean. A friend lent me a bottle of 70% rubbing alcohol. At first, it seemed to do the trick. The keys freed right up and I let it sit for a few hours.
If anyone is reading this and plans on cleaning a typewriter soon, let me be clear: DO NOT use 70% alcohol!
I never gave thought to what the other 30% was. When I came back, the joints in the type basket were rusted! Sure enough, on the back of the bottle, the principle inactive ingredient was purified water.
The first thing I did was go into panic mode.
Nooooo! I've ruined my new typewriter! I'll never get to hear it click and clack! I'll never use it to write a novel! Stupid jungle! Stupid quicksand!
Then, I consulted an expert: Richard Polt, a fellow typewriter enthusiast with loads of experience and free advise at his website here.
Richard gave me a sure-fire recipe to fix my problem. I sped to the local hardware store and picked up a bottle of carburetor cleaner and some denatured alcohol. A few squirts of the carb cleaner took care of the rust and the alcohol seems to be working on the keys.
Some of the keys are still sluggish. I sat down and typed a letter last night. Keys like P, T, and the period need more attention. They don't fall free after striking the platen. If I typed too fast, the machine would jam. However, I love the touch and feel of these keys. Once I get the keys completely gunk free, I'm sure it'll type like a sewing machine.
Most enthusiast websites claim that no one can predict how many alcohol rubs it takes to clean the keys. I'll just have to keep trying until I succeed.
Power to the pen!