Epson SC-P600, is there any way to take control?

[The Hat]

Doesn't seem like there is any software or firmware that will give me this option though, at least from my research, so looks like I'm stuck with it

I know this is an obvious answer but have you considered switching to a Canon printer, they are less likely to suffer from poor printout quality after a cleaning cycles, and they are far also less troublesome, in my opinion..
A clog is something you wear rather than suffer from..