oldhiker: I do think there is an issue in the lottery software, but there is no way for me to verify that until next year. Next year, I'll record the numbers of open slots right after the lottery is run, before people can decline their slots. Then we will have some solid numbers. At this point, it is not worth worrying about.
In the meantime, you can try to get what you want in the April 1 rush. But also, if you and your friends all came to Lone Pine, I can guarantee that you would get permits to hike as a group in 2 or 3 days, and most likely on the first day you try.
So just plan on taking several days, and you are good to go. There are plenty of other places to day hike to get acclimated -- you would be best doing that anyway for several days before the Whitney hike.