Because each contract was identical verbatim, is it fair to assume
that each new contract superseded the previous? Can I make this
I think that the more plausible interpretation would be that each contract applies to the move in question. So, if you quit 15 months after the last move, which is 20 months after the second to last move and 25 months after the first move, you would have to reimburse the company for the last two moves, but not the first one.
On the other hand, it would also be reasonable to argue that when you remained employed continuously between the first and second move, and between the second and third move, that a fair reading of the contract should not allow the company to require you to reimburse it for the first or second move, because your termination of employment after the third move would have no causal relationship to the money the company incurred in the first two moves.
One could also argue that the first two moves were a "penalty" which was void as against public policy because it was unrelated to the triggering event of termination of employment, or that the company should be estopped from asserting the charges for the first two moves because it forced them to happen.
I wouldn't be money on how the case would come out in the face of legal challenges like this one. Novation of the first two contracts, as the question suggests, isn't impossible to imagine prevailing either, but I wouldn't find it to be the most compelling theory.