See the other thread on a 9890 head issue that's in discussion concurrently with yours. If your nozzle checks look like those of the OP in that thread, specifically in the characteristics I pointed out, I suggest the head indeed is dead. I've seen that specific failure pattern on 11880 heads, and x900 heads. I haven't run or worked with any x890 printers, but their heads are the same at the core, as far as I know. This type of failure on these heads is not related to printing volume or even age of the head, it seems to be able to strike pretty well any time.
Any form of cleaning is a reasonable approach if the problem is one that can be fixed by cleaning.
The trick is diagnosing from whatever print flaws are visible, what the underlying cause is, or could be. Sometimes that diagnosis can't be made, and so we try various things to see what might work. My experience is the specific pattern of flawed nozzle check prints shown in the other thread is not a symptom of any kind of clog, air in the ink lines, pressure system failure, etc. but rather of a failed head.
And yes, I agree that Epson support is not too useful. (Also true of most other big companies these days.) We have a good Decision One tech in our local area and have called him out a couple of times to handle things I prefer not to do myself -- mainly just head replacements. No regrets in either of those instances. But mostly now I self-support. If research into a problem with any of our LF printers leads me to believe I can get parts and have a shot at fixing things myself, that's what I try first.
Modern LF printers are amazing when they work. Once they go sour, it's time to prepare to spend more cash, or else take the time to roll up one's sleeves for some research and DIY maintenance. All in my opinion of course...