I dared...
Collected latest drivers and software from the epson.com site (rather than from my local country one); cleared out all existing Epson drivers, printers and software then re-installed from the downloads.
Print driver
Scan driver
Scan OCR
Remote print
Software updater
Spent a bit of time configuring them...
...and - they all works fine now. Hard to understand what the problem was.
Good luck to all who still have issues - keep at it!