The YMCA here does a "Boot Camp" class that I attend every once in a while. I would consider it a CrossFit alternative. It's high-intensity, full body, and repetitious, with kettlebells, body weight lifts, burpees, etc. I've never seen any of the serious Olympic-style lifting that CrossFit incorporates, but I think it's a similar idea overall.
Like you, I'm primarily engaged in other activities, so it wouldn't be worth to me to pay for this separately even if I really enjoyed it (I don't). But we belong to the Y anyway for the children's programs, so this class is basically free to me. It's a good way to get a workout when it's cold outside and I don't feel like running.
So maybe check that out. Also, if you already own the kettlebells, I bet there are plenty of online subscriptions or even YouTube videos you could find that would provide a decent workout. If this is mostly to supplement your cycling, that seems like it would be sufficient. I would guess people pay for CrossFit largely for the community and the equipment. If those aren't motivators for you, this seems like a great job for the internet.