Close them quick as you can, if it takes you a week, then so be it, you'll come through. Like you said, you're making money anyway, its just you're having to give it back to the corps to keep them alive.
Suppose one good thing about winning that C3 war would be a GC boost for reaching WL2 and a bit of money out of the C3. I would not recommend keeping it yet, get one country going first.