Advice for an extrovert?

It took me a long time to realize what an extrovert I am.  I did the Gallup Strengths Finder recently, and in my top five were: Connectedness, Communication, and Winning Others Over.  I'm one of those people who is very energized by exchanging ideas with others socially, and I love working with small groups on projects at work.

The problem is, I'm divorced, and have teens who are at the age they want to do their own thing much of the time. I feel like I have an early empty nest - it's like I lost so much family life, almost all at once. They may feel that way too.  I don't want another partner right now. I have my kids most of the time, so dating seems impractical and only barely appealing.  I have connected with my friends in a deeper way (and made new ones), I have a strong (non-local) extended family, and I get to work with groups and individuals professionally, which is rewarding. But it's still not enough.

Suggestions? I'm working full time and in school, so it's hard to imagine starting a regular volunteer activity or club or ... I feel busy and tired - but I know how sustaining that sense of connection is for me when I get it.  I do feel like there's something missing.  A friend said "you can't rely on your kids for your social life" - ouch.  But true. Just hard to make that transition from family being 99% of my life to it being 20%, even though it's been over a year since the divorce.  Maybe others have experienced something similar and have ideas?