Like Peter, I have a long line of nonprofit IT Director/CIO jobs on my resume.
Currently, I'm the IT Director for a Community Action Agency. We've got about 20 programs ranging from Head Start to Home Weatherization and First-Time Homebuyer's classes.
Like you, all of these programs share a common finance, HR, and IT infrastructure.
I agree with Peter's assessment wholeheartedly (as I normally do).
I just wanted to share some of my experience on how to get there.. In a perfect world, the system Peter describes would be a dictate from the CEO that everyone would follow. In my experience, you're going to have to help build a culture that makes IT the centerpiece of these discussions. A lot of it will depend on you building relationships with the heads of these departments such that whenever the topic of technology comes up, their first thought is "let me get Karintha in on this discussion".
When it comes to my veto of software and hardware standards, I try to never say "No". I say, "let me put together the best way to get you what you want."
When it comes to users veto of functionality, I try to get into the process as early as possible. When I run into other directors or managers in the hall, I'll actually ask them if they have any projects coming up that I need to know about "so I can make sure I schedule the appropriate resources to your project". As soon as I am inside I lay out what IT's needs are and from there i tell them "you're the ones that will be working with this all day. I have these needs that I can't compromise on and outside of that I'm just here to help."
As for the C-level staff it's an easy argument to make. Following these guidelines costs less, gets you better customer service, and no one wants to be "that agency" in the newspaper.
Good luck, We're all rooting for you.