How serious are you about your girlfriend? It seems like the opportunity you were waiting for is here but you're looking for reasons to poke holes in it. If you aren't serious about the girl, move on so you both can take a step closer to finding the right person. If you are serious about this relationship, don't call her and say "Hi Sweetie, I have a job that would allow me to move out to be with you but after careful analysis I realize it will cost me $4,500 a year because of HCOL and loss of benefits. Sorry.", just move out there and be with her!
If you are having difficulty with this decision because of the fear of change, that is completely normal and you need to decide whether you can deal with the short term stress of moving, starting a new job etc. for the potential benefit of growing this relationship, having more satisfying work, etc. There are no guarantees in life, you may move out there and the relationship will fade or you may hate your new job but that doesn't mean you shouldn't take some calculated risks in life.
Finally, this is a money oriented blog and we all think about money a lot here but remember the point of FIRE is gaining independence so you don't have to run your life making decisions purely from a financial standpoint. Keep making financially responsible decisions but make decisions that make you happy and that don't jeopardize your long term financial situation. It sounds like you will be making a financial sacrifice but that does not necessarily mean it is a financially irresponsible decision. One of my favorite things that MMM ever wrote was about how early retirement has probably cost him at least $1 million dollars so far! If you embrace FIRE you are going to leave a lot more than $4,500 on the table at some point.
I'm not trying to talk you into doing this move, I just think from a financial perspective the options are so similar that your decision should be more based on whether you want to maintain the relationship with your girlfriend and the other non-financial factors. Also keep in my mind that if things don't work out with the job, the girl, or California there are going to be other options available to you that you can't even imagine right now.