Ugh, this can be tough. I think that there is a good chance that he isn’t completely aware of how he is coming off. He may be “too interested” but may not realize how it is being perceived. That doesn’t make it OK of course, but it can help dictate how you approach him. I know that for me, if I was in his place, I may have an understanding of who I was talking with but a lot of the “interacting” would be done in my mind while I was alone and a lot of what he’s feeling may have nothing to do with the real person but a scenario in his head. This may be very uncomfortable for him. It may be a lot of thoughts and voices that are loud and annoying and acting out this idea of liking this woman is the only way to calm them. His view of how things are going are likely different. His perception of social interactions in general is likely fractured. This can be a very sore subject for him, and if he is attacked on his ability to interact with other people, he may become very defensive.
I understand that you have many reasons for why this group could benefit him, but it’s a group and therefore is for many others as well. If he has now become too interested in a staff member it is important to try to redirect his thinking ASAP - before he becomes more involved. Don’t rely on social cues you would use on most people, he likely cannot read them the same way. Being direct is very important, and can be done very respectfully.
I would confront him about this this way:
After a meeting, meet with him and maybe another staff member if you have one available - a male staff member may be perfect, if he is fixed on a female staff member having a male there can help with his own ego. If he’s made “advances,” having a female confront him is likely not going to help you out. This isn’t an attack on him, you sound like you really want to be able to help him, you just need to make sure that everyone else is safe too.
I would see if the male staff (if this is possible) could talk to him one-on-one briefly and just sort of gauge where his mind is. He can ask how he feels about the rest of the staff and have that lead into a more direct inquiry on the staff member he is showing interest in. Invite HIM to tell you what HE is feeling. Ask what his goals are, what he wants to get out of the group. Explain that this is a community event and that everyone has different specific circumstances but that they are all there for support. Once he has been able to be heard, explain that the way the meetings work is that the staff can’t interact with group attendees outside of the group. Make it understood that this isn’t a special restriction for just him, it’s a universal rule. Mention that staff so-and-so was a little uncomfortable by his advances. Explain that she and everyone else there wants to help him and get him on a good path, just like everyone else. Remind him that this is a group, and that a group can offer support from all kinds of people but in order for it to work, EVERYONE needs to feel welcome.
See how he reacts to any of this. If he is unmedicated you can ask if he has a doctor he likes and what the doctor thinks about his situation. Tell him that medication may be able to help him and offer him some resources (pamphlets or the number of a doctor’s office or whatever services your area has/uses) so that he can try some sort of treatment in addition to the group. Really make this about wanting to help him. You can be firm, but kind, he has to follow the same rules as everyone else. Remember that in order to have a successful group, everyone needs to feel safe. If one member is rocking the boat, the best option can be to not have that member attend anymore (if he refuses to listen/change his behavior). If it turns out that he needs to stop attending, see if you can recommend another place for him to go.
I’d do this ASAP before it goes further. He likely has additional “encounters” with this woman in his head, and many of the things he thinks about her may be exaggerations and ideations. Snap him into reality before he goes deeper into his own world. If he continues to approach this woman, then you will need to take additional action of course, but this is my idea for how to confront him.
I hope some of this helps. A lot of people fall through the cracks because their behavior has been deemed too odd or dangerous. If they are just tossed out they will only go deeper into themselves and start causing problems for others. It’s admirable that you have asked for a way to help him not rudely. Hopefully you can help direct him to someone who can help him more intensively so he doesn’t end up just wandering in his own head.