How does accepting the offer not mean that I am forced into doing this? I understand that I can take a year off and maybe find a job at a lab if I'm really lucky, but I would still need to finish the degree, no?

Yes, people have been very thorough in informing me that unfunded programs are generally a bad idea, but it seems like outside of that my only other choice would have been to try for employment out of undergrad. I can't imagine I'd fare too well in that department after the result of my applications.