Success! The clog is cleared and I now have a perfect nozzle check pattern!
I used one of the specialty brands of inkjet cleaner (AIS, it simply was the first to arrive) with some foam stick wipes on the 'blade' head for LC.
Two goes with cleaning fluid, plus cleaning the wiper and cap station, and it was done.
What helped a lot is the newer generation printers have a 'Head Maintenance' option, that shifts the head way over to the left, where there's an easily removable panel (2 thumbscrews) so you can get direct access underneath to clean etc. I was wary of even touching it with a soft swab, but no problems.
No idea why Epson don't suggest this as part of their support, when regular cleans don't work.
Thanks all for your help.