Piercing Thunder and Primal Fury deal a lot with charge attacks. For an example, Bronze Lancet Charge, a level 1 Piercing Thunder maneuver does damage as normal +1d6. If you choose to bullrush instead of dealing damage with this maneuver, would you still get the bonus damage?
No. You have to follow what the strike says, so you cannot replace it with a bull rush without some other ability to allow you to do so. Like how a Magus can replace a touch attack for a spell with a weapon attack or, in some cases, combat maneuver.