For the purposes of this theory, we are assuming that a) the characters on Bill's Wheel are Dipper, Grunkle Stan, Wendy, Soos, Old Man McGucket, Robbie, Mabel, Pacifica, the author, and Gideon and b) Bill's Wheel is a prophecy that all 10 of these characters will eventually join together to either help fulfill Bill's master plan, or defeat him once and for all. We don't know which.
If all the characters will have to work together, they will have to be on the same team. Dipper, Mabel, Stanford, Soos and Wendy were always on the same team. Since Society of the Blind Eye, McGucket, Robbie, Pacifica and the author have joined that team. That leaves just one: Gideon. Which leads me to believe that Gideon will eventually be redeemed himself.
Now, Robbie's main conflict was with Dipper. But his redemption came through Mabel. The reverse is true for Pacifica: her main conflict was with Mabel, but her redemption came through Dipper. So, if Gideon's main conflict is with Stanford, it would only make sense that his redemption will come through Stanley (or whatever the author's name is.)
So, with that in place, I say that Stanley will end up sacrificing himself for his family. This would do four things. First, it would allow him to get up close and personal with Gideon Gleeful, since they will both be in prison. Second, it will get the cops off Grunkle Stan's back, allowing him to resume his normal life. Third, it will keep the author from revealing too many secrets too fast. Fourth, it will effectively take the author out of the picture until the writers want him back.
