Simply said, probably one of the better plans I've seen, it's the fact you have thought this through. Nothing wrong with completing your degree, starting a job in that field, and getting your ratings while you work. Honestly it will probably push you harder to do better.
Also, you can build up some savings for when you can finally jump into aviation full time, that is worth a lot. I never really had any savings until I got my 2nd job flying freight. Even then I wasn't making a lot, but it wasn't peanuts either.
There's a million ways to do it, and everyone's path is different, so good luck!