There is absolutely no requirement that your passport be close to expiration to get a new one. I think if you were willing to pay the $55, you could get a new one immediately after getting a passport, probably without giving any reason. You enclose the old passport and it gets canceled as part of the process.

On the other hand, if the photo isn't a good match, it doesn't seem to be a problem, so I'd suggest saving the $$$ and going with the photo currently in there.