Hello Steve, nice to hear from you again!
You have no less experience than I have, so you surely know that most gramophones play at their best with the records and soundbox for which their horn was "engineered" (= ear-tuned in most cases, especially for earlier machines). Acoustic-era machines plays exceptionally well acoustic records, but perform well only with some electrically recorded records (as a side note, I still have to understand why some electrically recorded records sound wonderfully on acoustic-era machines, and others only so and so).
You might try to temporarily install (for example with electrical tape) a different soundbox on your BIs and see if the sound improves or not. I'ts a trial-and-error process.
I accidentally made the reverse-test lately with a Decca Salon 130, a remarkable orthophonic machine that for one reason or another came to me with a wrong mica-diaphragm soundbox. The machine sounded awfully, but as soon as I equipped it with a period-correct aluminium soundbox it transformed into one of the best sounding machines that I own. As I also have mica-diaphragm machines that sounds wonderfully, what I understood is that the most important thing is that the soundbox and the horn match each other (either because they were carefully engineered, or by mere chance).
SteveM wrote:
What I think I might like to do is, trade my two Columbia BI Sterlings for one HMV 32 (if I can find one), and perform with just a 32 and a 102. I think the visual contrast would be fun and interesting for the audience, and I'm pretty sure I'd be happier with the sound.
I frankly discourage you to do so. Average people understand nothing about sound quality and music in general, you'll possibly be the only one in the room hearing any difference. Your two BIs are a marvel to look at and almost no other gramophone (all times, all makes) will match them in terms of visual quality. I believe your shows will be deprived if you switch to lesser-looking machines.