OK, I'm back home and the first thing that must be said is that huge apologies are in order.
Now that I've had some time to properly test, I must admit with great chagrin that there is nothing wrong. Applying the sample rate to all sources as per your suggestion fixes everything.
The reason I made the mistake is even more embarrassing.
I downloaded a particular CD, a CD which I later acquired and encoded to mp3 for myself. However, I didn't delete the old download. Thinking that it was MY encode, I did my tests using it. My mp3s are encoded with LAME 3.98.2 and the gapless flag. The download wasn't. No matter what I played it on, it wouldn't have been gapless - a fact I have verified now. Now that I'm home and have properly gotten all my ducks in a row, I can report that the WASAPI plugin does NOT break gapless and that applying the sample rate universally also stops the "stop at the end of a track" problem.
AGAIN, my sincere apologies, especially to Ian for wasting his valuable time.
Mea Culpa, Robert Culpa.