Hi Julia,
For us, when we started EASY when my LO was a little over 3 months, we implemented the routine first in hopes that the routine may help fix his sleep problems. Once we had our routine almost set, then we started on his nap problems and night wakings. I agree that you shouldn't do everything at the same time that would be too overwhelming for your LO and you. I think once you have implemented your EASY routine, then you can look at how you can change or tweak your routine that may help with your LO's sleeping problems. As you will find out, every board will ask you to post your schedule/routine to help with any problems you maybe having with your LO. So you might as well start with the routine first.
HTH
Mel