Update:
The 0.8w LED bulbs, I have put as many as (4) on a single lamp module and they still are dim when off. Adding more bulbs on the same module makes them negligibly dimmer. A barely noticeable difference. They dont seem to create any issues with the bulbs or modules and for now I'm just living with it. Since the lamps in question are all designed to be decorative more than functional it's not problematic yet. Right now I have 10 of them in operation on 3 modules.
The Kichler PAR30's . . . I have two on one appliance (since the bulbs are not dimmable) module along with an offbrand R20 that IS dimmable. With the module off, the R20 ALSO glows dim, even with the other two larger bulbs in the circuit. When I disconnect the PAR20, I can no longer turn off the module. When I turn it off from either controller, a few seconds pass and it cycles back on. I am going to try swapping the bulbs and the module.
I havent found instructions on how to disable the local control circuit on the appliance modules or the non standard lamp modules.