No worries, I understand what's going on now. I'd just hate to give advice to fix a problem I'm not fully understanding!
Good, so since the lights all function fine by themselves I don't think there is anything mechanically wrong with any of the units. I think you're right - the Quad Phase seems to be causing the problem. Adding that the Quad Phase can control the UFOs means that there is definitely some sort of signal or signals traveling through the chain when DMX is lost and that the Quad Phase is trying to be the master. Like you said with the different behavior in the Master/Blackout/Last modes, this might just be something you'll have to live with. Maybe keep it on last so at least you know your UFOs will work properly? How often do you really lose DMX?
One last suggestion though - does the physical order of the units make any difference? Try the order of UFO - UFO - Quad Phase. Do both UFOs act weird now? Then try Quad Phase - UFO - UFO. See if you can now control both UFOs.
I know that typically you'd want to use the shortest amount of cable in a DMX daisy chain, but in this case you might have to use a little extra to get the units to work how you want. Beyond this, you'd be looking at additional equipment (such as a splitter) that can isolate the Quad Phase from the UFOs. Who knows? Maybe ADJ will see this is a problem and release a firmware update for the Quad Phase so it plays nicely with other units. Hope it all works out!