Yes, tough situation.
Regarding your original question, I don’t believe getting mean will help and more likely hurt your cause. You have very little leverage at this point so they could just stop being cooperative at all. They may be more inclined to go above and beyond if you’re nice and convey the financial situation this puts you in (gain sympathy for your situation).
One avenue is to work with them on costs. Can they do the work at their cost? This splits the costs and is better than nothing. It also keeps them incentivized to keep working with NAPA on the warranty to get their money back (and yours as well).
Be aware you could be throwing good money after bad. Overheating almost always results in damage. Even surfacing the head to restore it is no guarantee it will result in a lasting repair as one example. The entire financial picture needs to be evaluated and only you can do that effectively.
Good luck!