I would say that if you see a possibility of recognition 2-3 levels up then you should be the leader that they need. You mentioned "large" so this may be the unlikely option.

However, if you see a chance of leveling up your career faster than in a job you love (but slower advancement), then you should "take over" and put the "owner hat" on -- what decision would the owner (or the board or the shareholders) of this company do and do that. Even if you are 10% better than the next person, that should be evident to the people around you and if this will be visible to people that matter.

You are getting PAID to do a job so you can complain about the job not being right for YOU but a "professional" makes sure that you are doing the job to benefit the company first. Even if it is not with your current position, this attitude and outlook will reward you eventually.

Good luck!