You could black box the solution so that all existing decision making mechanisms are retained and to every related system it is as if nothing has changed. To do this, calculate the projected cost for the life of the army as if that were the up front recruitment cost used in the current system. Life of the army = how long an army currently would go before its cohesion would run out without topup. If you wanted, you could failsafe disbanding the army at that point of time. The projected cost would also be subtracted from the influence balance for the purpose of influence based decisions while the army exists, and if it disbands for some other reason before its projected lifetime, that outstanding "virtual" balance is reconciled.
That may sound complex, but as programming design problems go, it's trivial.
Also, black boxing is not the approach I would actually recommend, it just demonstrates that the concern of unintended consequences has an answer.