It was the extractor.
As I posted earlier, on Friday I took it to the range and fired somewhere around 150 rounds through it without a singe failure. I took and home and cleaned it up. On Saturday morning I had a USPSA match. I got through the first stage perfectly, but I got 4 jams on the second stage alone. These jams were different from the ones I was experiencing earlier. They seemed like failures to extract. Unfortunately, my mind was racing a mile a minute out there and I don't recall exactly what they looked like. I took the gun apart and tried to clean it the best I could before stage 5, where I only had 1 jam.
So, I brought it back home and didn't clean it. I took it to the range today (Sunday) and fired almost 50 rounds until I could recreate the jam. Basically, after the round is fired, the extractor begins to extract the brass, but when the brass impacts the front of the brass from the top round in the magazine, the extractor slips off of the extracting brass. The slide goes all the way back, continues forward, then tries to feed the next round, but it can't because the brass that was failed to extract is still partway in the chamber. I put a picture of it at the bottom of this post.
I installed the old extractor and fired probably about 30 more rounds. I tried loading the magazines with 8 rounds and all fed fine. I tried loading the mags with just 2 rounds and they all fed fine. I finally got 1 failure to eject about half way through with probably 5 rounds left in the magazine. I would've taken a picture, but it was exactly like the FTEs I was having in the beginning of this thread. I cleared the jam and fired probably another 100 - 150 rounds without a problem, again with different number of bullets in the magazines.
Now, like I said earlier, I'm not a gunsmith. I'm just an idiot with a file and I really took a file to this new extractor that I installed. I fit the rear part to the firing pin stop (IMHO, I did that part pretty well), then I also filed down the very tip (the curved part) because it was impacting the side of the case, making the case not sit flush with the breech face. I have a feeling I filed down too much of the curve and only left enough metal to barely have a grip on the case.