I have found it is less stressful to wait until after the lottery is over say around March 15, check the availablity at
http://www.fs.fed.us/r5/inyo/recreation/wild/whitneyavail.shtml , call up the NPS, (they are very helpful after the rush is over), and make and pay for a reservation over the phone. I have always been able to get a permit up the main trail or MR for myself and a few friends. Yes, you may not get a weekend, but I think it is worth taking a few days off work to avoid the traffic and crowds.