How to start a new randomized level.

I'm working on a modification of the Basic Unity Platformer Tutorial, with the intent of making it more like an endless arcade-game with score tracking and whatnot. I have managed to successfully implement score-keeping and an HUD, as well as alter the level generation script to account for higher subsequent levels having more platforms and/or higher chance of falling platforms spawning (as opposed to stable platforms). What I have not found, however, is a way to actually create a new level once the player finishes the old one.

I had planned to create a sort of Goal platform guaranteed to spawn last on every level that would trigger a script to refresh the level while incrementing a "level" variable and retaining the player's current score, but I have met with little to no success in this venture. Does anyone know of any way to make this work, preferably using a function similar to Application.LoadLevel()?