Hey, I don’t have an answer for you, but I’m posting a similar thread with slightly different specifics. You didn’t mention anything about Google Home (which I assume you have because Chromecast). I have similar problems to yours, but mine seem to revolve around Google Home stealing focus, as in, PlexAmp stops showing it’s connected to whatever, but if I open the Home app and choose media the currently playing song shows, and it may or may not allow me to pause, skip, etc.
Might not be related to your issue, but figured I’d mention it. Here’s the link to the topic I just now posted… How do I stop Google Home from stealing "focus" while casting? . Perhaps we’ll find an answer there, eventually. Good luck.
Oh yeah, evidently we have vaguely similar musical taste!