I would protect the wire against the bracket using a short section of pvc hose (Home Depot/ACE/etc) that fits tight on the wire - slightly smalled inside diameter than the wire is best. Then cut it lengthwise to fit it over the wire. If you want it even better, you can first tie the hose to the wire at both ends and tie it to the bracket in the middle.Made an L bracket to mount to that longer stud on the left side. I'll move the wiring over to the left side and use zip ties or something (not sure) to secure the wire and connector to it. (I'll take recommendations other than zip ties)
Oh, sorry now I realized that you can secure the connector instead as you moved the wire. In this case I would use a harness clamp with a screw to the bracket. There are metal clamps of different diameters that may match the connector circumference. They usually have a inner plastic or rubber sleeve or you can cover them with electrical hose. That will prevent the conector from sliping out of the clamp.
Here is what I'm talking about:
You can find it at hardware stores, or local auto parts.