I solved the issue, at least for the Sparky 2 clones. The Sparky 2 schematic that I have specs an LP2992 voltage regulator, but my board has a MIC5219. The different regulator isn't a problem, in fact is supports higher current, but it is not necessarily a drop-in replacement for the LP2992. For example, the MIC5219 suggests a 470pF capacitor for a bypass capacitor, and the LP2992 specifies 10nF, which is what is on the Sparky 2 schematics.
My guess is that the cloners replaced the voltage regulator without changing the capacitor values and installed a 10nF capacitor, which is 20 times higher than recommended. I believe this is causing the voltage regulator to not regulate properly and was causing the (relatively) low frequency noise on the Vcc line, and was causing the fluctuations in the baro readings.
I completely removed the capacitor and now the baro is stable to within about a meter, which is much better. The MIC5219 will work without a bypass capacitor, but a 470pF capacitor could help lower the noise even more.
The bypass capacitor is the small capacitor directly in front of the regulator.
I somehow fried my Revo clone, so I can't test if that has the same problem, but it is probably worth investigating.