I guess I'm out of the woods enough that I can give the final story for my two guys here. They definitely did not get it swimming. It was the dead of winter and hadn't been swimming in at least four months, nor had they shared a bathtub with anyone, or even each other. Their cousin did have it at that time, though, although they had not played "contact" play with him.
Anyway, the older of the two got it first, and his never left his legs and lasted about six months. The younger one got it a few months later and it lasted at least a year. I used lemon myrtle oil on them (but not consistently - I'd get fed up with the bumps and use LMO daily for two weeks and then forget about it again), and I do think that helped, but can't be totally sure since I wasn't meticulous or scientific about it, lol.
I never could figure out how to pop them - I only once or twice saw any at the "angry red" stage (but I wasn't checking regularly) and when I did, it wasn't at a time I could do anything about it (containing the goo, etc.), and I'd forget about it by the time I could. So no popping, no scarring, now they're gone. The one who had them longer is definitely one who has a weaker immune system.
Neither has ever had measles or the MMR or chicken pox vaccine. I think the older had a few vaxes before I stopped by his first birthday. He was 5 or 6 when he got the molloscum. The younger had no vaxes at all.
My other children (one older than these two, one younger) did not ever get MC.