Wilson Farms
We have 2 25' 8200 heads , both work very well , But the first thing we do when anything is delivered is go over them from end to end , top to bottom. ( I know the dealers are supposed to , but it is hard to believe how many things you will find out of spec)
Most Dealers usually try to make sure the PDI etc is done correctly but most don't actually get out and run these things, we find that we get the service manual from the dealer and re do the PDI ourselves and make sure everything is set as per the book, The timing marks are noted in the service manual as part of the PDI , obviously your dealer over looked that section , which we find happens more often than it should.
Your stabilizer arms will have a threaded swivel ball on each end , it doesn't take much wear in the ends to make it shake, we keep a 1/2 dozen ends and at least 1 complete stabilizer rod in the tool box of the heads.
Another thing to check is the RPM of your drive , if you run them too fast they act like you have mentioned. I forgot to lock up our variable speed header drive once when on the flex head , and I ended up spending some $ to fix the knife up.