There is no way we would allow a sysadmin to patch anything at any time without some level of oversight
Change management is not your enemy
First let me say I really like it when people like what they do, and it sounds like you like what you do, take it seriously, and probably do it well.
However, this being a techy site, the commenters, yourself included, seem to inflate the importance of the one thing that is irrellivant and incidental. And by that I mean, of course, the system, the OS, and whatever state it may be in. Let me repeat, the OS is irrellivant and incidental. Thus, any time, effort, meetings, plans, etc., focusing on them at the expense of the state of what is important are an incredible waste of time and resources. I don't mean to belittle your job, btw, but merely to point out what every commenter I have looked at on this story seems to miss. The damn systems don't matter! (I am a systems admininstrator, myself, btw).
What matters? The data.
Change management is, in its own way, important for the reasons it is important and not for what those who have positively described it here. It is important because it tells us: "What the Hell have we done? How did we get here? What the Hell are we doing? Now what?" It is history, and it is intent. But it should only be as important as the systems themselves. And, again, the systems themselves don't matter one whit, especially if you have emergency procedures for when something breaks (i.e. fix it, or if fixing it is going to take too much time or effort, just reinstall it). So if you have a change-management-heavy operation, you're wasting a lot of time and effort for no great benefit or reason at all.
Tell me, at your company, is there a group whose sole responsibility is to manage the Data, and provide oversight concerning its reliability or how it is used or managed by the systems or users? Well, then its crazy that any resources would be sacrificed for the sake of the systems.
Systems administrators and the IT department are like the teams of airline mechanics. They're very specialized and very good at what they do because, in a relative way of course, lives depend on it. But what is important is not the damn planes but the cargo... i.e. in getting someone or something from point A to point B successfully. Does it matter if the plane is 40 years old? Not really, if that 40 year old plane does an identical job to a brand new plane. And we can replace the planes with high-speed trains, or (hopefully someday) teleportation. The planes themselves, and the use of them, are incidental, and irrelevant; they don't really matter.
In conclusion, I wouldn't say to the OP "get a new job!" as others have. That's not very helpful. I'd say, if you have control over these systems, and now you have to champion each new patch and get every patch approved, then switch everything to a system that will require less patches. Running Windows servers? Migrate to linux or a *nix variant. You'll still get security patches and bug fixes coming down, but far far less than with a Microsoft based operation, and if you miss a few months of patches, nothing really bad will happen (like on a Windows system). The world will still turn and the work will continue.