Homesick...I feel your pain! I too worked all the way through my CPL training while also completing a degree. I think that working and flying only when you have the cash may be a bit counter-productive as if your breaks between flying are too long, you will be 1 step behind again. This only adds to the final cost as you will have to pay for catch up flights too. I worked for a small regional airline doing everything ground ops which helped pay for my training to some degree, I also had saved up a bit from my job prior to starting my training but in the end I also decided to take out a loan. My loan is only about half of what you quoted but is such that my repayments are only approx $390 per month. Although I hate the thought of carrying this debt, it is not that hard to make the min repayments & even on a GA wage I often pay more than the min.
Each persons situation is different so you need to decide what's going to be best for you but if you have a job lined up at the end of it all then at least that's one less thing to worry about! Good luck with the rest of your training!