I guess this is just an opinion thing.
I'm not sold on this - I like the idea of the office of Governor having more prestige with a four month term. Otherwise it just seems as if he's a Representative with a veto pen instead of a vote.
I don't really see the case for that; he'd have all the powers that the Governor currently has, but simply have to face election more. If say we had a Governor who won four terms in a row under the proposed system, it might even be more prestigious than a Governor who won two terms in a row under the current system, if that makes sense.
That would make the poster more prestigious, not the office itself.
As it stands the powers of Governor are fairly limited and I think giving him as long of a term as the Representatives would just dilute the office further.