Setting the Movement speed, to something other than 0, of the submerged/burrowed unit allows it to move but also shows the units model instead of it looking as if it were underground.
Edit: giving the underground unit the Zone Indicator model, which is blank, solves the problem of the units model appearing when moving but it also means you cant actually select the model ingame, so i would recommend using another model that isnt the submerged naga and burrowed crypt fiend or a blank model, another model such as the arrow used by the shop sharing ability would suffice, but something else would probably be better as a moving arrow may look out of place in a map