But if you need to pick something up at JR in NRT then you might get stuck behind a queue of tourists spending 45 min at the travel center with the agents in doing their JR pass travel planning. I guess you can try to cut the queue.

I would just try to get on the first possible NEX. I suppose if you have a 10+ min time window before the NEX then you can work the machines and book the Shinkansen as well.

My understanding is that you are free to rebook on the same day, so I don't think you will be relegated to the unreserved section. I once took an earlier train and I just went up to the window and rebooked it. The green car rarely fills up. Maybe the rules are different if you miss your train.