Never heard of URD.... (On the west coast) googled it and came up with mostly med. voltage cable. (KV) You're right though, "Triplex" is pretty generic, and means diferent things to people. I think of it as arial service drop wire. "Triplexed", would be concentric clockwise twisted conductors in my mind.
Anyway you would have more room than you need to pull 3 4/0....(yes it won't be easy with distance and bends) Unless you are dealing with POCO rules like PG&E. You might be looking at 4"....
"Well - I oughta....." -Jackie Gleason