A couple things:
How large a group are you talking about, and ages?
Keep in mind that all permits are released at 7am, six months prior to the entry date. They are usually taken within 5 minutes and then a "W' or walkin appears which means the 'W' are released 2 weeks prior to entry date.
My experience this year with reserving permits is to be flexible with dates. It has really become difficult to get a permit for a popular entry point.
Lastly, enter the Whitney lottery, it can't hurt.
paul
