At 12k your current headset is very young, if it isn't notchy when you actually steer the bike my money is on the tire. There was a lot of tread left on my original Bridgestone Wobblemaster when I replaced it with a new Avon and it was like riding a new bike.
I've put All Balls kits in two old bikes and the result is creamy smooth steering. One day I'll be doing the same to my America but that won't be any time soon.
