The problem is not having just one instance open all the links. It seems it might be possible to hack around that by writing your own url handler for your os, then dispatching to the correct instance. (https://superuser.com/questions/119014/how-to-remotely-open-...)
But, as you say, the problem with that is that it doesn't handle opening links correctly.
I could see if I could write a URL handler that queries the window manager to find the last Firefox window that had focus on the current desktop (probably possible, but I'm unfamiliar with that domain)... or I could view Firefox not supporting this natively as a sign that it doesn't think my use case is very important, and stick with a browser that works without jumping through hoops.
It's not that I'm averse to putting some work in, per se -- I'm now in the middle of poking at writing a Firefox add-on to see if I can fix my complaints about insufficiently sticky containers -- it's just that writing my own OS url handler is a bit too hacky for my tastes.
https://github.com/kemayo/firefox-sticky-containers
I'm currently seeing whether #webextensions on irc.mozilla.org feels like ripping it to shreds, but I'll put it up on AMO after that's done.
No keyboard shortcuts to speak of.
I currently use Chrome's account profiles for this, so I have a desktop where my work profile lives and a desktop where my personal profile lives, and this makes links followed from other applications Just Work so long as I'm on the right desktop for them. I could probably get used to a slightly more awkward workflow, and the history being annoyingly shared between them, but...
EDIT: ah, well, I found the relevant github issue. Looks like there's years of arguing yet to go! https://github.com/mozilla/multi-account-containers/issues/3...