Old mechanical chime keeps randomly sounding after install, stopped after disconnecting power conditioner

I recently installed a ring pro 2 doorbell and the (very old) mechanical chime was going off occasionally by itself, without the button being pressed and without sounding the installed Ring Chimes or sending alerts. I confirmed several times there was no short anywhere. The only thing that made it stop was disconnecting the power conditioner. Background: The mechanical chime was a relatively fancy one for its day, about 50 years old or so. It's one of those with it's own mechanical programs for different doorbells. It has its own transformer on it (separate and downstream from the main power transformer in the closet to run the system) to run those programs, one of them is the traditional westminster chimes, it has different one for the side doorbell. When I first attempted the install there wasn't enough power even before installing the Ring doorbell device to start up the chime. I replaced the old system 16V transformer with a 40V one and that seemed to solve it at first. Then I installed the pro 2 doorbell and everything seemed fine at first, but then the mechanical doorbell would start going off by itself at odd intervals without the Ring devices activating. I checked to make sure there were no shorts on any end of the system. The power conditioner was installed securely across the COM and TRANS pins in the doorbell. Nothing solved the random mechanical chime issue until I pulled one of the power conditioner terminals. The Ring Pro 2 appears to still be working normally but I assume long term it wants that power conditioner installed. Is it possible that this power conditioner is letting enough power bleed through across the COM and TRANS terminals to build enough power in the old mechanical chime's little transformer to start the mechanical chime program? If so is the only solution to replace the old mechanical chime entirely? We'd like to continue using a mechanical bell as well as the Ring Chimes. Soon I plan to install another pro2 on the side door, and at that point I can just disable the mechanical chime and rely on the Ring Chimes, but until then we need the mechanical chime to sound for the manual side doorbell. And again we'd like to keep using a mechanical bell in the system. Is there some other way we can install the power conditioner or do we need to replace the old mechanical chime?