FWIW, I think you've done the right thing in rejecting the printer.
Your story is similar to mine, with an SC-P7500 (7570 in the USA). It was hauled up two flights of stairs and set up. Only PK and MK lines worked. Epson engineer came out the next day and recommended removal and replacement. Dealer objected (it had taken over an hour to get it up the stairs in my house, which are narrow and have a right-angle turn), and persuaded Epson to try to repair it. Epson engineer came out, with loads of parts, and after a whole day had it almost working. Returned the next day to replace the print head but after a quick clean, all nozzles were fine so I agreed there was no point.
All was then well for a couple of weeks, after which nozzle checks started to fail repeatedly. Another Epson engineer came out, replaced the head and couldn't get it to function, so I rejected the printer. I gave the dealer the choice between refund and replacement: he chose refund and the thing was duly taken away.
I was then away for a couple of months but ordered a replacement when I returned (and was out of quarantine), from a different dealer (of course). They broke a couple of plastic parts getting it up the stairs, which didn't affect function and were replaced within a few days, but otherwise the new printer has worked perfectly from the outset.
The whole experience was very irritating, and if I'd been relying on it for my business I'd have been furious. However, I have ended up with a printer for which I paid £240 less (the price had dropped) and has a 3-year rather than a 1-year warranty (change in standard practice by Epson in the interim); and the first engineer brought a complete set of 350ml cartridges, worth over £1,000, which of course I retained. So, swings and roundabouts.
Jeremy