This is not word games or Da Vinci Code. Far from it. It's the first principle of Biblical interpretation.
Did you ever wonder what that "I give you the keys to the Kingdom of Heaven" actually means? The most basic way to find out is to search the Bible itself for other instances of a person being given keys, or given authority under a king, and get a solid grasp of the Biblical culture to which it refers ("Interpret Scripture through Scripture.")
A suzerain is a viceroy who reigns in the king's stead when the king is away. He holds the keys to the Kingdom -- actually, the king's household and what would he his administrative offices --- and makes sure thigs are done properly according to the king's decree.
Eliakim isn't the only one who has this sort of delegated position. In Genesis, Jacob's son Joseph had this level of authority in relation to the Pharaoh of Egypy.
Each of these are images --- not exact duplicates or prescriptions, but images --- of delegated authority.
This is the kind of situation Jesus Christ, heir to the throne of David, was talking about when he entrusted the "keys of the kingdom" to Peter.
It is essential, when trying to understand Biblical teachings, to understand Biblical culture. It's not code: knowing the culture is an exegetical requirement.
I'll give you an A for originality and color