Firstly the error in my test for whether the mains earth affects loop impedance or not was indeed due to the mains lead of the function generator. I learned a good lesson. So,
I was wrong. It does not affect the ground loop impedance. Just to clarify again that when I say ground loop impedance I am not defining ground loop. but simply the ground path that I sketched out in my diagram above.
However, before continuing with the rest of the stuff I would like to mention that I have initially amended my first post with regards to Thor. Whatever happened has happened and I would not like to go there. I am taking my share of the blame by dismissing his mains cable improvements and not concentrating well. Put it onto Covid that I had. He is welcome to comment if he wishes to. My motto has always been that there can be a good thing coming out of bad, and this has been an opportunity for me to look into something that I would normally have not done so.
I will also be amending my first post with regards to the errors. I will not delete any text. I will cross them over and update with the correct info.
However, I have made a bit of investigation on some hi-fi equipment that I had in my clutter shelf today. These all have figure of 8 or cable terminated mains power entry. So, older Class 2 and with no safety earth. I measured the DC resistance on the chassis between the mains entry point (where normally IEC and earth stud point would have been) and the ground/screen tab of the input/output RCA connector. Essentially I measured DC resistance over a straight line. For this see below diagram.
1. Rotel power amplifier:
On this amp the RCA connector has no electrical connection to the equipment casing/chassis. So the resistance on the chassis on a straight line between the RCA ground and the point near the mains entry measured around 9.5 milliohms. On the other hand, I opened the casing and measured the DC resistance between the ground input connection post on the PCB and RCA and it measured around 220 milliohm.
2. Technics power amplifier:
This actually is a modern surround amplifier that I had rescued from our local civic amenity a couple of years ago. I could not believe why would anybody throw away a thing like that.
Anyhow, on this one the RCA connectors have electrical connection to the equipment case. Again the resistance on the chassis on a straight line between the (input) RCA ground and the point near the mains entry measured around 69 milliohms. I have not taken any internal measurements on this.
3. Technics CD player:
This is a bit older equipment that was given to me by our downstairs neighbour. Again the RCA has an electrical connection to the chassis, and the resistance on the chassis on a straight line between the RCA ground and the point near the mains entry measured around 15.6 milliohms.
4. Turbosound crossover:
This is (naturally) a balanced equipment with IEC mains power entry. Surprisingly the PIN 1 on the input XLRs are not connected to the chassis at all. I would assume the reason is to eliminate possible ground loops to form. But there can be a price to pay for that too of course. However, the resistance between the earth tab on the IEC and PIN 1 on the output XLRs measured around 89 milliohms.
The distance between these measurement points are below 50cm. So, I measured the resistance of a 50cm length ordinary single strand 0.8mm2 hook-up wire, which gave about 16.6 milliohms.
I also had a couple of reels of medical grade 1mm2 multi strand Alpha hook-up wire that were used on a control system that I had designed (20 years ago) for an industrial dishwasher prototype. 50 cm length measured 9.65 milliohms.
Now, you'll probably anticipate where I am going with these wires. It seems clear that even on old Class 2 audio equipment the internal ground paths (Ground Path A and A' on the diagram in my first post) can be vastly reduced in impedance. Of course such modification would warrant compliance. So, why not replace mains entry with IEC for Class 1. Particularly on Rotel. The chassis resistance will shunt the actual ground path and give a better path impedance figure.
In terms of external reduction method for Class 1 by using low impedance earth wire, as I mentioned before, it is clear that the contact resistances dominate. I have no idea on what sort of premium connectors are available and their contact resistances are. I'll need to investigate.
As for the signal connections between two (ore more) equipment, an external low impedance wire in parallel to the screen as in the link given by Newmarket also clearly brings considerable improvement.
Finally, credit should be given where it is due. In my case to Thor for paving way to the subject.
EDIT: The first post became too cluttered. I have edited it completely but with an amended diagram.