RFK fields is a great venue for this for various reasons. They'll be booked weekday afternoons during the season, but could largely be free during the offseason and you can usually find space on the weekends. The reservation calendar is available online so you should have a good idea when you can find free space.
I've organized games with my kid's former teammates in the past pretty successfully. I based the invites on lists from his first and second clubs (ages 7-12). As the kids changed clubs they were able to bring teammates and friends as well. And at that age, the more athletic parents can play to help fill out the ranks.
https://eventsdc.com/venue/fields-rfk-campus/calendar[url]