Hey Steve, I would never try to feed AC neutral anywhere on a coax shield.
That's just too dangerous.
In 1968, I purchased 6 meter rec converter from an old Ham.
It came with a DIY power supply. It was a plain metal box with a transformer on top.
It worked fine, so I never opened the box.. It had a non-polarized AC plug.
After a near disaster, I opened the box and found the transformer was only
6.3vac for the tube's filaments! The 170VDC B+ for the tube plates
was directly rectified right off the grid!!
The neutral side of the plug was the box ground.
The hot line connected to a big diode and a cap.
The day I plugged it in the wrong way, it was snowing and raining.
The hot side was on the outside coax shield. I never noticed anything.
Later I heard on the scanner, 'A power line has fallen on the fences'..
My neighbor told me that there was sparks when he closed the gate.
I then realized, The 6M antenna was on the fence!
I disconnected the converter and opened the box.. Dang!
I ran out and told the power company guys what happened.
They were glad to get out of the weather.
My wife heard on the scanner, "Some ham radio nut had power connected to his fence".
All the fences on the block were connected together. And, all the steel poles
were sitting in wet concrete blocks in the wet ground.
All that ground should have shorted and blown the 15A fuse in the basement.
I went down and checked it the next day. It was blown!
It had been blown before we moved in..
But, some other tenant had placed a penny behind it..
I looked over both basement fuse boxes and found 4 more pennies!