I just can't see Eickhoff anywhere near that high. It has been several years since he has been healthy and even his good year was due to favorable luck. Arrieta is an interesting question. Clearly he belongs at number two based on history and durability and even what he did last year. If I were looking to the future though I might position the rotation as:
Nola, Pivetta, Velasquez, Arrieta, Eflin, Eickhoff. Beyond that I don't think it matters much. De Los Santos could easily be a bullpen option so it might be Suarez as the next up depending on how everyone pitches. Velasquez certainly could be moved to the bullpen if the team acquires another starter. Absent that though, he pitched almost as well as Pivetta last year and has the potential to do better. I think the bullpen move would be to create an Andrew Miller-type multi-inning reliever which is not necessarily a demotion given bullpen usage these days (a 90-inning multi-inning reliever might be more important than a 120-130 inning 5th starter that goes 4 innings every time.
In general I feel good about our top 5. Eickhoff if healthy is a fine back end option as well. I would go with this rotation and re-evaluate whether a midseason move needs to be made around the end of May.