Wow; thanks for all the responses. I guess my SG and I are wierder than we thought..
We're all set-in-our-ways curmudgeons and only play teams formed exclusively from our SG ranks.
Due to the lack of a "share mission" feature, and to enjoy its automatic level-matching, we've adopted the practice of doing nearly all of our missions via the Oroboros mechanisms. Yes, the team could all just tag along on any member's mission, but not if they all would like to earn the Merit rewards from an arc.
Owing to real-life time pressures, not everyone whose toon begins an Oroboros TF is always able to make it online for each gaming session. When such conflicts arise, we leave the toons that began the impacted TFs logged out, form up a different set of alts into another team, and begin a TF with them.
We very seldom finish task forces in just one gaming session.
At any given time, we usually have three or four different task forces underway, pending the availability of the guild members that made them up.
As others have pointed out, the "who's on what TF" information can be kept on paper records or spreadsheets (and we've tried), but we're just not that disciplined. So when we convene on our voicechat for a gaming session, there's usually a lot of fumbling around, as each of us logs in one alt after another, looking for a combination that suits the particular group of logged-in players.
The wish list feature I've tried to describe would be very much welcomed by my group of player-friends, but I gather from the responses so far that we're too much of an edge case. Thanks, anyway.