Hi Cary-
This may be after the fact, but if so, it may help someone else....
We were just there a month ago. We made our reservations about two days in advance via phone from Rothenberg and had a reservation #, so the situation is different. Two thoughts, however. If possible, call to confirm and get the question answered (since you are already in Europe). That way you know you are set and can confirm which time. If not, just stick with your plan of going early enough. When you pick up the tickets move to the windows on the far right, for reserved tickets. The multitude of chains seems daunting, but we just zoomed right up.
Aside: 1) Ask for a map there--we missed them and had to back-track. We found the map helpful, but actually POOR for the level and intensity of this tourism site. We walked everywhere--on paths that did not exist on the map.
2) Waiting in the heat at Neu. for your time was challenging, so wear a hat, sunscreen and bring water. We walked to the bridge, too. We recommend.
3) There is a Bavarian castle pass that we bought in Wurzburg at the Residenz, but can be bought at whatever the first castle you visit is (that is included in the pass). Seeing 3 castles makes it pay for itself, if I remember right. ONE of the two castles, either Hohen. or Neu was included, but not the other. So, we only paid for one, but handling fee for both, I believe. Enjoy!--it's crowded, but so memorable.