Shortly after the game was released I made a little speedrun (Intended as a walkthrough at first) for people who were stuck. Played through the game, very unoptimised and doesn't even finish, in about 2½ hours. Found
here.
My intentions after that has been to make an actual TAS. I wanted to wait for the 2.0 release that SePH was working on before. He has stated that he might return to it one day. Possibly after finishing the hack he is currently working on:
http://parallelsequel.wordpress.com/
If I made a TAS with the current version of the game (1.1) I would have to climb the Parallel Tower three times. Which will be highly annoying looking in a run I can imagine. As well as the many bugs that may occur while playing the game. So that's why I have yet not started a full run.
I made a glitched TAS three years ago however, same boring run as the ALttP glitched:
http://dehacked.2y.net/microstorage.php/info/191537828/ParallelWorldsGlitchedTAS.smv
Also, Franpa, what exactly is your purpose with the playthrough? It doesn't really feel like it has anything to do with either speedrunning or TASing the game.