Well a 12 ga extension cord,,, It may be possible to route it through existing holes in the floor and not even have to drill. 12 ga has less voltage drop.
Now, look at your water lines,, If they drop through the floor at any point (The waste lines clearly do) there may be enough room in that hole to sneak one end of the extension cord through.. Then depending on your trailer you can route it into an outdoor compartment, or you can terminate it there (Buy the proper length cord) and use a 2nd 12ga cord to the pedestal. I have one such cord installed... I do not use it often (Since I have other choices) but when the temps drop below 20.. I need all the power I can get.