There will be times when fate and luck screw over even "real men" you can't win em all bro.
Case in point: Kamina.
As for the drama... uh. I'm inclined to agree that fitting in the (full) UFO crew would be difficult, especially given the implications of retconning in the game's events and what they would have meant for some character interactions. For that matter, UFO was apparently supposed to occur during late spring/early summer, while Dream is set during early spring.
I guess we could try to work with it as the spring AFTER that, but there are probably still a few complications... then again, with Sho already having Kogasa without people getting confused at who she is, that may be a valid counterpoint.
It might be doable... but it's something that'd take a lot of planning on a broad scale.
Either way, if further UFO characters ARE used, it's definitely a bad idea to retcon them into existing crews. New 'battery' characters,
random discoveries (not this late please Tenshi was iffy enough) or currently-implausible-and-or-unsafe rescues from RAI and otherwise are a safer bet.
Of course, MTG could also work them into the plot (whats-her-name, the final boss, is particularly relevant to the Covenant schtick and could very well have gotten involved with that other Covenant(?) faction MTG mentioned), which should probably take priority in this case.
One loophole for new characters at this point (that I was hoping to bring up in-story first) is people that saved a Gensokyoite but left the Karuisuwa area. Having them return would take some hand-waving or other explanations, but it's a plausible excuse - especially if they were visitors to the area that didn't live there, or at least one of their group considered it safer to at least temporarily flee the area.
This is actually a plan I had for, like, a female
high-schooler scholastic ronin (failed college entrance exams and taking a year to study for next time) otaku character that took in Nazrin as an unusually intelligent pet ala Orin, but with more random theft of shiny things. Then again, I'm overworking myself enough already.
---
tl;dr MTG's got his work cut out for him planning what to do about UFO to make sure the game's events don't interfere with what's already happened, and we definitely can't retcon in any more of UFO's characters to existing teams without a good explanation.
As for claimingness, I'd consider writing quality to be a good meta-level indicator of worthiness, and balancing out a team's combat abilities not. Plausible connections to existing teammates is valid. Having more people writing would be a mixed blessing; another person to keep track of and informed about RP events (and making sure they have a good grasp of what's occurred), but no increased burden on writing, relationship mapping, or character management for the existing players... I'm not sure how that balances out.
The only plausible excuse for existing-team joining for the UFO crew at this point would be rescuing from another faction, which would probably have to be a team effort and leave linking choice pretty much up for grabs. And be very, very, VERY dangerous to security circumstances. Sorry guys, I'm not sure it's a good idea.