Can I move a GFCI outlet from the end of a circuit to the middle to protect another oulet?
You could move the GFCI outlet to the center box and have it protect a regular outlet by the sink.  A GFCI outlet has "line" and "load" terminals.  The line side is for the incoming power.  Load is for downstream, regular outlets that need protection.

Pigtail both outlets to the load side of the GFI in the center box. They don't need to be in a linear chain or anything.