Huge, I went through something like this last year - easiest to describe as some play in the bars just as you bring the bike to a halt/release the brake. I got similar answers to above, none of which helped my problem. I eventually decided to get the race head bearings changed. Apologies for the overly technical description of what fixed it - they told me that as soon as they started to take it apart they found some clip/ring/nut/something underneath the main assembly that was cracked. Replacing that sorted it, and was a lot cheaper than the job it was booked in for. Whatever had broken couldn't be seen until other bits were removed... However, sounds like you've already had yours stripped and they didn't see this...