Then again, if the USA was formed exactly as it did in history and republics start at 1% tradition, if one does not get to over 20% tradition within (4?) years that would automatically make George Washington a king with these mechanics. But we do not know how fast tradition can be gained anyway, so... oh well
Speaking offhand, one way of handling this could be an event popping up when you become a republic, asking if your glorious leader intends to rule for life - accepting would allow your initial revolutionary to rule for his lifetime, but with greatly reduced republican tradition gain, while refusing would let elections continue as normal.
One question, though - are election candidates still essentially random, or will past candidates and past doges come up again on the ticket later?