If you elect all of your regional legislators at the same time, you could consider the Northeast's solution to the electoral competitiveness problem: Grant the title of Lieutenant Governor to the legislator receiving the most votes in the prior election.
This doesn't work well if you have a large set of responsibilities and powers in mind, but if you're most interested in having someone to take the Governor's place in case of absence or resignation, it's an effective way of dealing with the situation.
The Speaker assumes Governorship if the Governor resigns or disappears, so that's already taken care of.
Then you have no Speaker.