Exercises such as the Voyer Shrug (explained in one of the Neanderthal No More articles) and snatch grip rack pulls will help.
However, ongoing effort in daily life to hold posture as well as possible -- regardless that it doesn't feel natural -- makes more of a difference than such exercises will. It is inherently a slow process.
But several months of being serious about this should yield quite noticeable improvement, with further improvement occurring with yet more time if you stick with it.
Also strive to notice and correct those instances where you habitually crane the head even more forward. Common examples are when driving or using the computer.
A major help can be in noticing yourself in TV screens where security cameras show people in line, etc. They provide a reality check that neither the mirror nor your "feel" does.
It's very unlikely that anything that doesn't have your chin pointed in the air is actually going to be an overcorrection. A given "I'm pulling my head back" position may feel like it could be too much to you, but it's unlikely at this point that even so it is actually all the way back to correct, let alone going past correct.