A degree is not the be all end all. It’s also definitely not ‘overqualified’. Some sort of post secondary, either college or university, is mostly normal. Those without either probably have some impressive work history- a few of the CAF vets I’ve seen get in fall into that category.
But yeah, as said above, the process is a long haul, and you’ll be graduated well before your file is reaching anything close to a first culling phase.
Do what you’re comfortable with. If that’s waiting a couple more months, all good. Though that could be a couple months earlier to retire on the other end. Weird way to think about it, but time is the thing you can’t reliably get more of. If your only concern is getting the paper on the wall first, I think we can all assure you that with how close you are, it’s not a concern.