And, for posterity, let it be known:
This method of changing government type works.
Especially with the rulership established by a vote instead of by random claiming. In a one-duchy realm where the ruler is the duke, the ruler can change the government system basically at will (change ruler voting to dukes only, step down, wait for anarchy, run for office, vote for self, win, change government).
With multiple duchies or less concentrated power it'd be trickier.