Negotiating Pay for NAF Position

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*UPDATE you can negotiate a NAF position and they met me half way.


Hello so I am switching from a NAF position to another NAF position that is a different job/title. They have offered me the exact same pay I am currently receiving. The offer letter does not leave room for negotiation portion. It's a check yes or check no. 

I am changing jobs due to wanting to leave my current location and so I am switching from Army to Navy. There is no relocation.  I  will be going to a lower cost of living. I honestly thought I was going to be taking at least a 10k pay cut and thrilled at even just the offer. I just don't want to get there and realize they are under paying me. The job I was offered had the same individual in it for the last 30 years so I know they were likely receiving  the top step pay. 

Can I still email the offeror and ask for an increase in pay? I briefly googled and it is mainly discussing GS positions. I assume they offered me the same pay thinking I will be satisfied. I am well qualified for this job and surpass the educational requirements and experience (by 4 years).