Alrighty, I got Leala's approval, so my Seanchan Ogier is posted now.
Some thoughts I have for him at this time are:
Ortun Idea 1: Just meet and befriend (on the surface at least) some characters, while he sketches and records details of the greater cities, waygates, etc.
Ortun Idea 2: In travels, perhaps he could reach Malkier and aid in the coming battle there, seeing firsthand the reality of the Shadow. Then in time, return to the Seanchan with revelations of shadowspawn and the Dark One. Possibly leading to uniting the Seanchan with the other nations against the shadow somewhere down the line. There's a lot to see and do before he reaches that far north though.
Ortun Idea 3: Make a ‘friend’ in his journeys and then down the line, because he ultimately serves the Empire, betray that friend to the Seanchan (perhaps an Aes Sedai made into damane, if anyone is interested?) but still show a protective nature if he witnesses a sul’dam acting out of line towards that friend.
Again, down the line. Lots to see and do before he returns to Ebou Dar.