Is there a way to purposefully freeze a process given a certain condition so that it doesn't leave the job queue until it is addressed manually?

No, there isn't. You can add a process step at the beginning that is only generated when the process should freeze. That process step can deliberately fail every time (SQLComponent, ScriptComponent, ...) as is marked to stop on error. Instead of restarting this job later, you choose to continue with the success path of the process in the JobQueueInfo.

But speaking generally, parking a process in the job queue is often not the best choice, as you potentially block some other calculations for this object. There is the view "Affected objects" in JobQueue for verification.