Is there a way for me to increase the OD size of a barrel connector without having to replace it?
The correct way would be to slip one or more tight fitting phosphor-bronze split sleeves over the plug but at some point the housing will prevent the larger diameter. However it is very unlikely that you would have such a sleeve in your junk box.  You could carefully cut a strip of brass shim stock to a width the length of the exposed metal barrel part of the plug and a few centimetres long.  Carefully and tightly wrapping this over the shank of a Philips or Torx screw driver shank (that has a drive end smaller than the shank) of lesser diameter than the plug.  Then remove the coil and with great care you cut a turn off after size testing on the plug. If the added thickness is enough you are ready or you may need to add more than one layer.  Be careful that the sleeve does not get stuck into the socket, a very small amount of cyano-acrylate glue could be used to stick it in place, let it wick into the open gaps and set without any movement so the metal to metal contact is undisturbed.

Perhaps the lateral thinkers on SE.lifehacks might have some ideas.  

The loosening socket problem is exacerbated when an oversized plug is forced into a socket also the centre pin is very often smaller on a larger plug so there will be poor contact there if this is attempted.