Thanks, Dave, for the comments on the possibilities around what could be causing this. On one occasion when I picked up the second line I was in my radio room and examined the waterfall display in the WSJT program. This time, there were no other strong signals competing with the 1st transmission segment. But I didn't analyze the other cases. It sounds like there isn't a reason in the power system for this - the way you have it set up, missed parts of transmission pairs would be randomly distributed. For now, I'll presume that it was a combination of randomness and some signal swamping.
The 30m antenna transmitting on 20m just generated another idea...Could a tiny LC trap be installed in the antenna to make it resonant on either band?
BTW, congratulations on your very cool achievement!