First you need to check if there is any runout caused at the sizing stage. I use a Lee collet die and it doesn't. Then you need to see if the seater will do its job properly.
Big issue is the shape of the seating stem plug. If it is shallow for lighter bullet, the Amax will not be supported during seating and runout is likely.
You can use any generic seater and get great results IF the stem is the right shape.
If the bullet tip bottoms in the stem before the ogive, deepen the cavity in the stem. This has to be done straight but a drill press can be made to work.
Take the stem out and put a bullet in. If the bullet nose does not touch the bottom of the stem, the chances of a bullet seating cockeyed is high.
Jerry