I'd say continue with your other degree, once completed get a good job then pay for your flying as you go on a non-integrated course, get command time rather than a swag of ratings if you want your resume to stand out. First jobs don't need multi, instrument etc, spend the money building command time and getting interesting experience. Networking is the key and even bag chucking can lead to something, I got my first flying job after meeting an employer when I was a gopher in a hangar, sweeping the floor.
Another bit of advice, words like "passion" and "obsession" don't really belong in an environment when you are operating heavy machinery. The industry needs pragmatic people, not dreamers. Good luck!