I don't think any effort whatsoever should be made to keep that team competitive. I was under the impression that it was simply "filler" so we could actually start the league. IMO, all the starter slots on that team should be left empty each week so that it functions like a bye. Unfortunately, it's already won a game, so changing that now wouldn't be particularly fair.
I also think next season, if we need another dummy team, you should make an effort to have it draft crappy players. It's not too difficult to set up a draft queue of players rated in the 1000's. When the team consists of nothing but third-string quarterbacks and guys on IR, we won't have to worry about things like this.