I think that if you use a convert that if you hit with a spell that hits overtime that overtime should change also.
Example: I am a Fire student so i use a Fire Prism then use Fire dragon. fire dragon hit the prism pops (w/e) to convert the hit to ICE. then the the over time hits also turn to ice and hit as ice for the next 3 rounds .
If you don't like your traps or prisms being used up with a DO t, find a different school. OR. Lay 4 converts. They may make a multiple convert sell in the future, but until then, no.