What about moving to 4 days on 4 off and doing 12 hour shifts? Once you have been there for 8 hours you may as well stay for 12!
I previously worked a combination of 4 days then 4 nights but as more people were needed in the day you didn't always have to do nights.
Glad I didn't have to do the 2 days 2 nights then 4 off combination as it meant you would be doing nights all the time. At least doing 4 in a row then 4 off and then days again means your body isn't so messed around!
If you have to keep the 3 shifts why not do NNNNNN XXX LLLLLL XXX EEEEEE
Harsh doing six nights in a row but then you have a long gap before you do anymore. And then have almost 4 days off going from an early to a night.