I don't seem to have an option to check "Finest Detail" -- perhaps it's for the same reason Epson doesn't seem to offer color profiles, seemly that they call it "multifunction" rather than "photo printer."
Anyhow, I definitely see sharper results when I print at 360 (as compared to not checking resolution) -- and 360 is also clearly better than 720 -- and I'd like to be able to use 720 if possible -- but I gather I need "Finest Detail" -- and I don't see where I can turn that on.