A bit of an update:
For the moment I'm sticking to 25m repeats and Mode 3.
I found that the upper limit is around 0:60 and am now exploring the lower limit
Today I worked my way down to 0:33 and was surprised to find that my last 50m ( 2x25m) was my fastest of the set (but still very slow, of course).
I am trying to eliminate the tendency to pull too early with my right arm, and so far the best approach seems to be to concentrate solely on the right arm and time the beeps with hand entry and hand exit. Also breathing as little as possible seems useful, which is not difficult at this slow tempo. Trying to breathe more often on the right-hand side is also probably a good idea.