jonorman has a good suggestion if you want a plugin.
However, you mentioned that you used the Drape Tool--not the Stamp Tool. Drape will conform to the terrain contours, whereas Stamp will modify the terrain as I indicated.
EDIT: If you choose not to get the plugin, which does have a free version, one possible "quick fix" could be to make a careful selection of the road elements only, perhaps copy away to the side, use the footprint to help form a more regular pavement ribbon, make it a component or group, position it above your terrain and run the Stamp Tool.