Hi Sebastian,
We still hire a very small percentage of pilots without the degree. The numbers I've seen are in the neighborhood of 2%.
So, that should tell you two things:
Apply now, network like heck and get as many LOR's as you can. Do everything possible to enhance your professional quals. Facilitate anything they'll let you. Become an LCA. You know the drill. You might get lucky and get called.
But while you're doing that stuff, get your degree finished. Most motivated folks can knock out the Utah Valley BA in less than two years without killing yourself.
Just do it. But don't wait to apply either.
There are pilots here without the degree.
Good luck!