No there's no different option, only 1 contact length can be signed. In the case of Jeeves point 3, the expired contract is signed in season 1, so the contract will expire in (current season) +2 years. Just as when it says "contract will expire next season" it means (current season) +1 year.
Renewing during the last season (Will expire at end of season) or the grace period after expiration (Player is unsigned, not currently playable, X days to resign) will have the same result. Difference being the bonus and wage amounts.
You can keep a contract length as 3 if, for some reason, you choose to renew every season.