ChrisR the trick to get the change you need is to hit the button on the AND just before the first beat, this creates a visual change just perfect when you sing, if you hit TC on the notes you will find it hard to follow as you pointed out, 1&2&3&4& 1&2&3&4& hit your timecodes on the & after the 4 and you will notice a big difference in your following the lyrics on screen.
After a while this will be real easy to do and very natural as you know exactly what is going to be the end result.
The solution would be for this to be done automatically by the software so you can hit the TC on the beat but it seems to be too hard to program, the same applies in changing audio sections, ideally you want the lyrics to change slightly earlier before the audio so you can see the next lyrics on the & after the fourth beat so you are cofourtable to begin singing the next lyrics.
I have mentioned this problem ages ago but its not on the priority list but i think its very important to have a very smooth lyrics display functioning before other features are introduced as ST3 is already perfect for the majority of users.