This may be completely unrelated since my experience is with a Canon 6400, but I found a way to bypass a clean cycle so perhaps this might provide an idea for the Epson.
After the printer has been idle for about 3 days, I notice that it does an auto clean cycle whenever you eventually want to do a print. I have the auto nozzle check set to off, but if I don't use the printer every 2 days, it still wants to do this clean cycle first. Sometimes I forgot to print every 2 days, and it managed to not go through it after 3 days, but this is the upper boundary. Given the fact that a clean cycle wastes 12ml of ink, it is better to print something that uses only 1-2ml of ink every 2 days rather than to waste the 12ml of ink.
After being away for a week and having the printer off, I booted up in Service Mode and did a Service Mode nozzle check. (For non Canon folk, this is a different type of nozzle check which shows every single nozzle, even the ones that have been mapped to other nozzles). It didn't look good, which is to be expected, and some colors had easily a few dozen blocked nozzles. I immediately did another one, and it looked about 75% better.
The reason why I went through the Service Mode is because, as a result of going through other issues, I've noticed that lots of regular checks are turned off in Service Mode. It lets you do stuff that might otherwise not be possible. You of course can't print in Service Mode, but even if your printer refuses to do anything in regular mode, the Service Mode would allow you to print a nozzle check or other testing type things.
Anyway, so now my thinking was that even though the printer was turned off for a week, the service mode nozzle check actually moved some ink through it, and because it wasn't the regular mode, it wasn't inclined to run an auto clean which it would do after noticing that it had not been used for a few days. The critical thing is that now, the printer technically had just done a print, the nozzle check, so perhaps this would trick the printer into thinking that it really hadn't been 7 days since doing a print job.
I then booted up in regular mode, ran another nozzle check, and this one was perfect. I then proceeded to do my print, which it did, without having to do a clean cycle! I am back to printing every 2 days now, and if I ever miss this window, I will be sure to follow my steps again in the service mode. I will be going away again soon, so will have the printer off for another week, and hopefully I can get it up and running again without a clean cycle, which will also prove that this wasn't just a fluke.
Once again, I'm not sure how this might help with the Epson, but I see that even Wayne found a loophole when the cart was almost empty, so perhaps there would be a way through some service menu.