Ioannis,
I think I overlooked a new feature that was added to Map Suite 5. It is the property WrapDatelineMode of the Overlay. So, if you set this property to WrapDateLine any layer (Shapefile, InMemoryFeatureLayer etc) that you add is going to appear continuously as you pan to the west or to the east so that you can see the Pacific Rim with Japan to the left and California to the right. So, please check this Code Community sample Wrap Dateline Mode with Projection. In this sample, it also shows the projection aspect but you can ignore that if this is not relevant for your case. wiki.thinkgeo.com/wiki/Map_Suite_De...Projection
I think you might still want to split your shape as you see in the sample Polygon across Meridian and then apply the WrapDatelineMode property.
I also think that you might think interesting to check out other earlier samples concerning this issue with all the challenges it involves.
-Pacific Rim wiki.thinkgeo.com/wiki/Map_Suite_De...acific_Rim
-Great Circle on Pacific Rim wiki.thinkgeo.com/wiki/Map_Suite_De...acific_Rim
-Great Circle with Google Map wiki.thinkgeo.com/wiki/Map_Suite_De...Google_Map