If you're using 001 the A/D latency should only be 51 samples. I'd argue that the human hear can't hear that unless you're reamping which with bring about phase issues. If you're using M-Box it's a little bit more, but it's still something you probably wouldn't hear. If it's ProTools Free, I hear there's a zillion issues to deal with and I wouldn't know what to say.
I always use low latency monitoring when I record, but that helps with monitoring latency. If you're moving tracks it sounds to me like you're dealing with A/D conversion latency.
How far do you have to slide the tracks to get it synched?
What Pro Tools system are you using?