I was hoping the st- e3 would fire the 600 which would then fire by slave on the 580.
thats a bummer.
I'm having the same sort of issues, I have the 600 and 430 as well as 2 Yongnuo 622 triggers and would like to use both flash guns off camera but I think I'm a trigger short ?
not sure if it will work but you can set both the 600 and ste3 to work in the IR mode so it will be like using a STE2. They then may all take to each other but the range will be very limited.
ST-E3 doesn't have a light-code IR mode, though the 600EX-RT does.