As a challenge, this doesn't seem too hard to achieve. The easiest option would be for the King not to promise double numerical representation early on. Thus the Third Estate would not push for unicameralism as it would have nothing to gain by it.
Does anyone know why the King had this give-away of double representation in the first place? It seems like radicalism was not a force yet, and he was still firmly in control...
I'm also interested in the WI side of this. If they had to get a vote from one of the other estates, what things would pass and what would not? It seems likely that the First Estate would be the closest ally to the Third, but that would probably mean avoiding offending the church. Which two Estates would gang up on the other? Could a situation to the financial crisis be found, even if only short term?