All you can really do is hope that sooner or later his boss puts two and two together. In fact, they may have done in order to bring you on board with the remit you say you have been given. In light of that I supposed you could go through a document each mistake that has caused a project to overrun and hope that he is the common thread that unites all the projects.
Alternatively you could try getting the department to run within it's budget and force the necessary cuts be made to staff provisioning. This will force the IT manager to actually go round firing people. Since this is a very tough part of the job to do he might balk at it or at the very least screw it up in a way he can't blame on anyone else.
To be honest though this doesn't sound like you are entirely being truthful. If you were really in the position you are in you probably would have been given the right to fire the IT manager and recruit a decent replacement as part of the deal. This gives you the option to force him to raise his game and also help in with any additional training he needs to become a better manager.
When it come to firing managers you generally just pay them off and then give them gardening leave for the duration of their contract along with a cast iron reference they can take to another employer. This gives them a reason to go quietly without you proving they were shit at all.
If you do not have that and are effectively working under him or alongside him then you are on road to nowhere and might as well just concentrate on helping the department underneath him run well as best you can. Even an incredibly shit IT manager can look amazing if the department all know there stuff and do what they need to.
If projects are all necessarily complex that is not just the fault of the IT manager, that is also the fault of the person or people delivering them. Try working on them directly to get them to deliver better work, one possible way to do this is to subtly make them realise who is for the chop if the costs don't come down. Obviously you have to be very careful how you do this, it might help to pick one person who is on side already but also has a good working relationship with his colleagues and then drop a few hints.
If you are doing all this already and the IT manager is blocking you then you might end up in a situation where all you can do is take your consultancy fee and make a few suggestions around the edges.