Hm, quite strange. The Warrior does have a nose-wheel steering connected to rudder pedals (unlike Diamond/Cirrus and some other aircraft), so the required rudder input would be noticeably less than without the steering (while the nose wheel is one the ground of course). Even if the nose wheel steering would be inoperative (which I think you would notice during taxi), I don't think you would need full (or any significant) right rudder deflection - left rudder perhaps, but right rudder requirement seems a bit off (assuming right-hand prop rotation which most SE aircraft have). Usually with single-engine aircraft you have to give it a bit of left rudder when you retard throttle to idle before flare, since the engine isn't producing as much torque as it did during powered approach, but the fixed trim-tab on the rudder is still pushing the aircraft to the right, since it's usually set for cruise power/speed. I just remembered that some PA28s (perhaps all) are equipped with rudder trim, so you should ensure you're using the correct setting (if I remember correctly, I think for takeoff and landing it should be somewhere between center and quarter of full right deflection).
Given that the problem isn't as usual, I would do the next things:
- check the rudder trim tab / rudder trim setting before landing
- the amount of rudder (left or right) you are required during different phases of flight (takeoff just after rotation, climb, cruise, descent, approach, flare) to keep the ball centered
- ask the other pilots (preferrably someone more experienced) who fly the plane if they notice anything unusual: and if they don't, ask them to tell you how they fly the aircraft to do so
- have a chat with somebody in charge with maintenance of the aircraft, perhaps they know something you don't
P.S.: 1998 Piper Warrior is not vintage, in the spam-can GA market it's almost state of the art aircraft
