Does your state require public experience for the CPA or just accounting experience? Like if you left and went to private, could you use that for the experience requirement if your current employer refused to sign off down the road?
No matter how great your employer may seem right now, I've seen some of the best employment situations go really really sour after the 2 weeks' notice is given in. Generally I get along really well with my bosses – I'm the person that coworkers are likely to think must just be boss's favorite cause I do what bosses want done, and therefore bosses like me, and I usually have a good relationship with them. But…I've had a couple times that those great relationships get terrible after I gave notice. One job that on my last day I genuinely was worried my boss was going to get physical with me – he stood up from behind his desk and was doing the “puff out chest and try to look big” like a rooster preparing to fight. I left at 11am instead of working out the rest of the day in order to avoid a physical confrontation…and 2 weeks before, we'd gotten along great, and he'd thought I was awesome.
So, my point is, you never know what may change after you give your notice. The situation above is an extreme, for sure. However, for some reason, after people give notice, it seems like the environment changes and it's not at all uncommon for relationships that were good before to go a bit sour. You definitely still can get your sign-off after you leave, but you also can definitely lose it. If all that you lack for being licensed is passing FAR and BEC, then I'd stay put till you pass your last exams, get the signature, know for sure you're safe on the experience, and then move on. Unless you could get the experience at the next job, and if so, then if you're willing to risk having to wait a year to get a new year of experience, then go ahead and switch jobs before passing FAR and BEC.