I agree with mozar: it is truly a game, so play it. Check "yes" -- and then, if/when a promotion/transfer opportunity comes up, find some reason why it's not the right "fit" for you at the moment.
The problem is that companies very much value people who are "go-getters," who send the message that their career is the most important thing. So if you wave your arms around and insist that this is no longer you, you will likely be more and more marginalized over the next few years. And that makes those 4 years extend into eternity.
My DH just had this talk, btw. They are reorganizing and likely consolidating a bunch of related stuff under him, and he is very very excited about the tech and has a very clear vision of where he wants things to go, so having it all be his area will allow him to implement his vision more effectively. He also has a new-ish boss, who asked for a sit-down to discuss his career plans. DH -- being a frank, forthright person (a/k/a "engineer") -- told his boss that he loved that particular area, and that if a VP position came up in another department,* he wanted to stay in his current role instead.
You'd think the boss would be happy, right? Guy is so dedicated to what he is doing that he is prioritizing getting the work done right over his own personal advancement? Nope. The boss, in a nice way, told DH to re-think the message he was sending. Because the people in the company who get listened to are the people who are seen as up-and-comers. So if you remove yourself from the "up-and-comer" track and suggest that your career advancement isn't the top priority, you are no longer seen as smart/dedicated/driven/worthy, and so no one includes you or listens to what you have to say. So, ironically, DH's vocal dedication to getting his current job done right would actually deprive him of the power he needs within the company to do that. He has to play the game, and say all the right things, simply to accomplish what he wants to in his current role.
YMMV, of course. But something in your description of both you and your company suggests to me that you guys may operate similarly. So you may need to hone your skills in the art of creative bullshitting to make your remaining years there as satisfying as possible.
*Company's standard approach is to identify people for the VP track, and then promote them to that level whenever a slot -- any slot -- becomes open. As a result, taking the promotion almost always requires a transfer to a completely different area.