Lots to answer here! I'll hit some points, and if I miss a question anybody needs an answer to, please ask it again.
First off, you should always feel free as MC to ask the player to swap their obligation gig for a different, more fictionally current one. This isn't by the strictest interpretation of the rules, so if the player refuses you should shrug and move on, but it's by the next-to-strictest. So Shimrod, if it comes to it you can always just say "hey, this seeking answers thing, cross it off and write in 'keeping Newton and Fauna happy' instead, okay? You can get back to seeking answers whenever." That's your fallback.
Next up, the gig is seeking answers, generally and unspecified. Trying to find the legendary bunker is a perfect example of what seeking answers means for the operator here and now, but as MC, you don't limit your thinking to finding the bunker, you start slipping in clues right away that the bunker is just one piece of a much larger puzzle. That way, you can let the operator find the bunker just as soon as he legitimately would, you don't have to put him artificially off.
So he finds the bunker, and you've laid the groundwork for it to not be the final answer, but to raise tantalizing new questions. Now it's the player's choice whether to spend experience to resolve the obligation gig, declaring that the answer he was seeking really was just the location of the bunker, or else to leave the gig in effect and pursue the mystery beyond the bunker.
Okay! About the "obligation" part of the obligation gig: the only obligation that's required is the consequence of leaving the gig unworked. There doesn't need to be an obligation to another person, and there doesn't need to be any driving internal pressure. If the player feels comfy leaving the gig unworked and dealing with the consequences, that's fine, that's the choice he gets to make.
The consequence of leaving the gig unworked is on you, the MC, to create. For the seeking answers gig, the consequence of leaving it unworked is that the mystery deepens, with new clues that don't fit together. (This is good, it feeds directly into the above.) It's your job to make this happen and you should take this job seriously. The good news is that it's not your job to capture the player's interest and make him pursue the mystery after all, it's your job to make the mystery interesting to you, yourself. If you're having fun ramping up the mystery, and the player just keeps leaving it unworked, no sweat! You're having fun doing what you're doing and that's what's called for.
Concretely: you should write up the bunker as a threat, give it its impulse, and when the operator leaves the gig unworked, make one of its threat moves. It seems to me that Hare should be square in its crosshairs.
Then as the bunker develops in play, as its moves form a pattern and as you lay the groundwork for the deeper mystery, have an eye toward writing up the deeper mystery as a front, with the bunker as just the most prominent, first encountered threat.
Anyhow, go look at pages 139-140 right now, I think you'll find something you like.
-Vincent