I did almost the same last summer but went in via Piute Pass. I had gotten the entry permit 6 months out but was unable to the Trail Crest exit at that time. I came into Lone Pine a day early and was able to get both a entry and TC exit permit at the ranger station in Lone Pine. I believe you cant get a TC addon to your original permit. You must start over getting a new permit if the exit is available at that time. From the beta I have gathered mid week is the best time.
So you are saying you reserved JUST the entry permit for Piute Pass but didn't have a Whitney exit... then when you went to Bishiop to get the permit, you were at the office early, during the middle of the week, and asked for a Whitney exit and they gave it to you?
On the application for the Piute pass, what did you put as your exit point? Cottonwood?