Great reply from Privacy.
We were fully home ed from age 8 - 11, and since then my DD has been at a fully online secondary school. It really suits us because DD has her school friends (with whom she's very close, albeit the relationships are mainly conducted online) and still has the free time to attend a few home ed social groups and see the friends she made on the home ed scene. Of those home ed friends, there's a real spectrum from fully autonomous through to quite structured. We were lucky in that this never seemed to affect the friendships between the kids/parents. We were lucky enough to be included in an invitation to a gaming group, and that's now been going for 6 years (from cute kids playing minecraft to lanky teens playing WoW
). There's also a lovely social group where the kids tend to run in a feral gang do their own thing, and socialisation between parents isn't necessarily required.
A few thoughts/ideas...
Are there facebook groups for home ed in your area/county? If so, you've got a better chance of connecting with new people on there, I'd have thought, than in the groups you've been to lots of times before. If not - set one up!
How do you feel about being proactive and organising/hosting social/activity groups? A gaming club and a book club spring immediately to mind, given what you've said about their interests. Do they have any other interests at all? Anything they're interested in, get them into a club/short course if there's one around - they only need to make a good connection with one or two other kids, and voila - they've got friends.
For the older one, have they expressed any inclination to start more formal schooling? Doesn't have to be mainstream school (though it might be!), but online schooling, home ed cooperatives with group classes, small tutor groups. If you can find some other families to split the cost of a tutor with, then they'll form relationships with their fellow students. Online school?
I ran a weekly science club for a few months, helped out by a friend of mine who runs science after-school clubs. There was a group of half a dozen or so, and the other parents paid for the materiels and my friend's expenses. Doesn't have to go on indefinitely, but if you suggested a course of 10 sessions - it's quite doable to plan ten 'kitchen science' experiments, or biology sessions, or whatever - and split the cost of materials, I bet people would bite your hand off. Again, FB groups are the place to organise that stuff. In my experience, home edders will travel for stuff like that, too, so you might make connections with people a bit further afield in your county who you may not have met at local groups.