Would your current mentor still be willing to provide a letter if you leave, especially since you seem to have a good reason for leaving? Alternatively, would it be possible to continue working remotely? I don't know what your research and data collection processes are like, perhaps you could access the lab/data remotely and work on data analysis and manuscript writing from your new location. Additionally maybe a trusted research assistant could help continue your data collection.
For the record, I left a post-doc position after about 10 months. I realized once I got there that it wasn't going to work out as I had expected so I immediately started looking for something new. I too was geographically restricted so I understand how stressful this can be. I went on the job market without a letter from my initial mentor, though I count myself lucky that I was able to find a new group to work with quite quickly and I have a letter from my new mentor who I now have been working with for over a year (first as a collaborator, now full time). I've had a phone interview and it did come up, but they seemed quite understanding when I explained that my initial position was ultimately a poor fit and lacking in the appropriate research resources. But, I don't know if this has hurt me in my other applications. I should certainly hope that the same would occur in your case — if you can explain in an interview (or have another letter writer also explain a bit for you) I like to think most individuals would be understanding.