Green on 12V is NOT generally accepted as a NEGATIVE wire, period.
Bad form, followed by more bad form = epic fail.
RV 12V wiring uses WHITE for the negative, no other colors are used for that purpose.
All other colors including black are 12V POSITIVE..
What I would have done instead of all the haphazard hacking would be to run a new run using typical RV 12V wiring colors (white is neg and black or other colors are positive) from the 12V outlet to the CONVERTER fuse panel OR directly to the battery. I would have used 14 ga wire for a short run and possibly 12 ga wire for a longer run just to keep the voltage drop to a minimum.
At the converter I would have connected the negative directly to the negative terminal on the 12V FUSE PANEL. IF the fuse block does not have a negative terminal I would have traced the 12V negative out the BACK of the panel and then SPLICED there.
I would NEVER, EVER consider using the 120V side of the panel for this type of modifications even though the ground terminal in the 120V side is at the same potential it is not a good idea..
To put this another way, the 120V ground is for SAFETY, there is a BONDING wire that goes to the frame. This wire is typically 10 ga or 8 ga and is there only to ensure all metal of the trailer will be at 120V ground potential.
It is bad form due to the fact that someone else who is not familiar with YOUR modification may mistake that fake green wire for the wrong use.
While YOU don't see the error of your ways and feel it is "safe" you are voiding any and all NEC rules on keeping separation between 120V and low voltage systems just by having that fake green wire running into the 120V box..