My biggest hesitation with adding another dog is that he has never seemed to really enjoy the company of another dog. He basically ignores them, and then tries to play once in a blue moon.
Murphy is pretty much like this. He only plays once in awhile and only on his terms. Otherwise he pretty much ignores everyone (me included lol) and does his own thing. But I saw a HUGE difference in him when we got Mu. Once she grew out of the annoying puppy stage he went from being "there" to being fully present. He is much much happier in a multi-dog household.
(((((hugs))))) The situation sucks and it sounds like it's stressing you out as much as it's stressing Frodo out. Honestly, a lot of it sounds similar to what I did with the girls and it turned into a self fulfilling prophecy. I'd get home, angst about letting them out together, let them out together, micromanage their every move for fear something would happen, something WOULD happen (because I was micromanaging them), I would freak out, they would get separated, and we would be absolutely no further along. Only for Frodo it's going outside, or you leaving the apartment, or whatever. I think getting him evaluated and possibly on meds is a fantastic idea. I don't know if you've done this already but maybe a behaviorist would help?
ETA: I am NOT saying anything is your fault - I just reread what I wrote and it comes across that way. What I'm trying to say is that figuring out how and where to break that cycle of anxiety (for both of you) is important. It might be meds, it might be behavior work, but it does sound like you guys are stuck in a loop. Feel free to PM me if you want to, I know that feeling of "OMG nothing I do is working and we're going to be stuck doing this FOREVER and I hate it."