To begin with, I think that allowing maneuver aspects to stack up indefinitely is probably not a great idea. Maneuvers are supposed to be "momentary, situational advantages", and it's hard to see how a duration of 20 sessions fits into "momentary". So you need to either backtrack and 'correct' this, or go with your decisions up to now. It sounds to me as though you are fine with the way its going so far and would like to proceed from there. Fair enough!
First of all, a quick sanity check. If you decide to scale the 'hireling' based on the heavily modified roll (52 contacts, 56 resources), then the expectation is that the result will be POWERFUL. So think about how this will impact the game -- will the story benefit from the players being able to phone up, say Thor (or perhaps a small nation, if a less supernatural result is pursued) for fire support when necessary?
I think I'd be inclined to turn the whole situation into a storyline. Perhaps something along these lines:
The characters do their thing, spread around money, work contacts, etc. They get some responses, and they discard many of them. Eventually, however, they get a solid bite. They are approached by someone with significant resources of varying types, and is willing to hire them to the players for the price that they are offering. And the benefits look solid. Possibly no 'demigod-like', but solid. He has an information network that extends well into the supernatural realms. He has bodyguards that can be assigned to the characters -- not every session, perhaps, but when truly needed -- and the bodyguards are clearly more than mere human. He knows people who can make things happen, or who can "smooth over" problems that the players have, whether its the mortal police ... or perhaps even the White Council, assuming the situation isn't too serious.
The group, of course, grabs the opportunity. And make use of it. And perhaps come to depend on it, as the 'problems' the begin to face become more powerful than they themselves can handle.
Of course, they say that anything that seems too good to be true is probably just that. And so is the case here. It turns out that their 'hireling' is actually a demon (or insert chosen ickiness here), and he is actually using the players to his own advantage. As a demon, he is limited in what influence he can bring to bear on his own behalf, but he's much freer to act when others do the asking. So when the players ask for help clearing things up when one of them is arrested, they simply see the problem go away. They don't see the demon sending in a Malvora minion to kidnap the DA's child, coercing the DA to drop the charges, and returning the child in a near-catatonic state due to the Malvora's feedings. And so on.
So as time goes on, the demon grows stronger. In essence, the players are feeding him Fate points that he can't earn on his own. He starts to be a little less circumspect about his actions, and perhaps the players start noticing things. Or perhaps they notice that their reputation is starting to tarnish a bit, and wonder why. In any case, the end result is that they realize that their 'hireling' is actually the villain in the story, and is even creating some of the problems that they hire him to solve.
From there, either engineer a suitably interesting climactic showdown, or turn the demon into a long-term Threat, and leave it to the players to determine how to clean up the mess that they have unwittingly created...
Your mileage may vary...
