I'd definitely feel no issue applying for unemployment since that's why they suck that money out of the paychecks in the first place. I do understand the "Don't want to get a hand out" though. I've never gotten a dime from the government, and have no intention of doing so. But when you pay for years to unemployment, you might as well use it while you look for a new position.

Good luck finding the new job, I have no doubt you'll get hired because you sound like a hard worker.