How strange. I had to enter the repository URLs (now that I'm at the computer I can see it was Michael's Slim Stuff for the RP plugin and Philippe's LMS Plugins for the upnp bridge, both found after a bit of googling). Until I did so, nothing about Radio Paradise or UPnP bridges appeared in the plugins list. I'd also logged in via the mysqueezebox tab.
FWIW I just tried turning on automatic redirection to https in the Network>DSM settings page (and after it'd restarted, and Safari had had a heart attack), restarted LMS, and... No difference. The RP plugin still asks for the socket business. So I turned https redirection back off again, to save Safari any further trauma. And then gave up again.
The moral of the story seems to be that you might get lucky, but if you don't, be prepared for some IT guy stuff.