As a postscript to the above, I decided to disconnect everything and start all over again, using an Inverto 32-band Unicable II multiswitch (IDLU-UWT110-CUO10-32P). This now feeds 28.2E to all three receivers (GigaBlue UHD Quad 4K, Vu+ Solo 4K and Inverto Multibox SAT>IP server, connected via a three-way Dur-line splitter with power pass) -- which occupy 20 User Bands in all. And I was thrilled to find that they all worked straight away, with (so far) no tuning problems or other interactions, and no interrupted recordings. I am powering the Unicable switch over the downlead, using the supplied PSU and injector, to avoid uncertainty over relying on the receivers for power.
I don't know what was causing the problems I had earlier, though it can't have been any of the receivers or the Spaun Unicable I switch. Misconfiguration seems the most likely explanation, though I checked my settings no end of times. My thanks to posters in this thread for their advice.