I think, maybe, I might have found a working solution.
The setup described above stopped working completely, let alone just being unreliable. I think I have tried every known type of cable, adapter and interface (active and passive) but the Surface Dock never simply worked/s with them although there have been occasional glimmers of function. Latest drivers and Windows OS installed. I considered getting other monitors; would probably have been cheaper in the end than all the cables and adapters etc but would have been a relatively big expense in one lump and I had no faith that even an approved monitor would work.
I found that the Surface was becoming by far my least used device. I used my Samsung Note extensively - a better tablet anyway - and also used my desktop quite a lot. And the Surface only when there was no alternative. A much nicer device than my other laptop but equally under utilised.
But now, I hope, (and actually believe) I have a solution. I have attached another dock. This time a Plugable USB dock. I attached it first to the Surface and then to the Surface Dock and it simply worked as if working was never something to be questioned. I am using both docks mostly because I have them both, but prefer to avoid regularly attaching and detaching the dock to the USB port; the MS magnetic charger/connector is easily attached and detached without any mechanical stress on the port. It is very early days, and it might turn round and bite me, but it feels stable just as it ought to be.
It will mean I use the Surface very much more. I've been happy to use it for portability and when I'm just doing one thing, but I really like a lot of screen space for my usual multitasking.