Sounds like you're using cron as a complex job queue! A lot of teams get there eventually, and either 1) keep hacking on cron/jenkins/etc to make this work, 2) invent their own queueing tool (NIH syndrome; been done many times before, there is nothing new to make here), or 3) use a purpose-built solution for this. Airflow is the old-and-busted solution; the new hotness is newer generations of the same concept (Prefect/Dagster, Luigi, Temporal). But often sticking to your existing thing is cheaper; depends how much custom engineering you want to invest.

Fwiw, I do believe you can do this in GHA, but you may need to call their API from your workflow. In addition, their replacement for Groovy is to run an action which lets you embed Javascript/Typescript and call their SDK. It sucks, but so does Groovy! ;-)