So I finally screwed up my courage and made it out to a master's swim practice in the area. On the few days when I'm actually able to sleep in, it's hard to set my alarm back 30 minutes to try something new. But I'm almost certain that it'll be worth the effort; the swim instructor is really quite good, and able to build a little bit at a time where even my rather sleep deprived mind was able to follow.
Sadly however, I really have no idea how many laps I did. Many of them were in fins, too, so I'm not certain they count. My big problem is overusing my legs- the form useful in running is not so helpful in the water.
It is interesting to hear swimmers talk about "land athletes" however. It wasn't disrespectful... just a feeling of "ye are different than us." Difficult to put into words, really.