Thanks for the thread. It's something I have and will continue to deal with, myself. I'm an introvert, but like most introverts, I am a human being, so I have a need for closeness, connection, relationships -- just not a lot of them, and not as much as other people. (An aside - some people seem to be confusing introversion with having schizoid personality, which involves a lack of interest in close relationships).
I live in a fairly small town (about 50 to 100K), where most people think differently than I do (conservative religious, traditional "family values," etc.), so social groups (e.g., meetup) that appeal to me can be hard to find.
I'm still a ways off from downshifting my work hours, but I'm thinking through these issues. Here is what I'm thinking:
1. I love animals. My dog is a wonderful companion and my best friend. I feed the birds and squirrels in the backyard. I watch my dog chase the squirrels. When the birds and squirrels are gathered, squeaking and squawking, I realize I'm supporting a whole community. I never feel alone in my backyard. I never feel alone when I'm with my dog. We walk the neighborhood streets and visit the other dogs and cats, some of whom get chased and some of whom are our friends.
I imagine that when I have more time (I have yet to retire), I'll volunteer at one of the local animal shelters. Pets can be a huge source of comfort and companionship. We don't give them nearly enough credit for what intelligent, feeling creatures they are.
2. I believe that people/beings live beyond this material existence. I may not be able to see loved ones who have passed on, or guardian spirits, but I know they are there. In the broadest sense, God is there; I am in God. So I am, we are, never really alone. When I can remember that, it's a very expansive and gratifying realization.
3. I think doing your inner work is important -- that is, the first and most important relationship you have is the one with yourself. Do I sound like Oprah? I hope not. It's become such a cliche in our culture, but it's still true. You've got to be on good terms with yourself, otherwise you just act out roles unconsciously, project junk on to your friends/partners, etc.. So "working" on my relationship with myself is a priority for me. I think the upper limit of the quality of your relationships to others is set by the quality of your relationship to your self.
4. As far as finding relationships with others, I think most of the good suggestions have already been covered -- meetup groups, volunteering, taking a class, OLLI classes if there is an OLLI in your neighborhood, joining a church group if you can find one that fits you, dating sites, etc.
Good luck, and thanks again for the thread. Good subject, one I'm wrestling with myself.