I would check to make sure that new tire is seated all the way around. I've seen it happen before where the bead isn't seated all the way around. That would give you a vibration for sure. Don't know as it would cause a pull though.

I wondered why the frisbee was getting bigger......and then it hit me. '05 BA - Mulberry/Graphite,128 mains,42 pilots,TBS needles,drilled slides,debaffled stock pipes,Uni,no snorkel