Splitting up the shapefile won't really help you. The solution is to either create a web service out of the shapefile (by publishing it to ArcGIS Server) or finding a service out there already.
When you add a shapefile to a web map, the browser draws the features. The 1000 feature limit isn't on a per-layer basis. The total of ALL layers that you add to the map that are being drawn by the browser should be less than 1000. Actually, this feature limit is an estimate. If you have complex line or polygon geometry with a lot of vertices, the limit will be less. It's due to the browser's ability to handle the drawing.
Mike