I think the hesitation of your builder to fasten to your back wall is fear that the screws may pull out due to the cantilever leverage of the cabinets. Another approach is to build a cleat along the bulkhead wall between the galley and teardrop interior. add short cleats to the sidewalls and construct a shelf for your cabinets to sit on.
I build my galley cabinets in place. Below is a picture of the cleats that I used. The side cleats are screwed into 5/16" thick material. The bottom of the back cleat is fastened into 1/8" plywood and 3/4" framing. The top of the back cleat is fastened into 1/8" plywood only.

(If you do something like this, your cleats don't have to be that deep. An 1" to 1-1/2" would be sufficient. I had panels top and bottom of my cleats to form a space for cubby holes and a center drawer.)
This is a picture of my "shelf":

And here is the finished product:
