Recumbent trikes are generally slower than two wheeled recumbents and not all recumbent are fast. There are very different types of recumbents, from touring to racing types just like with upright bikes. 13Kph is really slow in my opinion and i only see those low speeds with elderly people here. I think everyone with a decent bike and a normal condition should be able to manage 20kph with ease.
If you have troubles with a sore bottom or sore wrists: get yourself a recumbent