Have the rules changed? It has been years since I did any big hikes, but it used to be that permits were by trailhead.
The last one I needed a permit for I left from Onion Valley (one trailhead north of Whitney portal I think). It was and I imagine still is the second most popular on hte East side of the range, second only to Whitney portal. Being solo helped me get in. But just one up from Onion Valley the trailhead was 4000 feet lower and no problem to get a pemit for. Also it seemed no bear problems, while leaving Onion Vaslley meant you had to make it over the pass and down the the bear boxes on the other side.
Just a thought, if you really want to do Whitney and if the rules are the same jsut take more time and start from farther away.
they established 'the mt. whitney zone' a few years back so regardless where you come from, if you enter the zone, you must apply for the lottery. doesn't matter if you hike west to east all the way from mineral king, do the jmt/pct from yosemite or just the whitney portal trail or go cross country from arc pass or mt. russell. personally, i prefer the sky blue lake area to the south, the kaweahs to the west, the kings-kern divide to the northwest and some of the forester pass/center basin area to the north but the entire area is stellar. definitely difficult to find solitude in the whitney area but you gotta do it at least once.
permits are still by trailhead for all the rest of the other trails. that mt. whitney area is like the longs peak area in rocky mountain natl park in colorado. it suxx but it's a necessary evil. the area is literally loved to death. yeah the onion valley/kearsarge pass trailhead has the 2nd or 3rd largest permit allocation (bishop pass is right up there too) but offers greater access to other areas so the traffic gets a little more diffused.
The BWCA is by lottery as well. They allow x number of people per day, where x varies my entry point. When I submitted mine, I got my first choice of entry point and day. But I was very punctual sending it in. I also picked an entry point that started with a half mile portage - I thought that might reduce the competition.
For Whitney, the lottery applies to entry dates between May 1 and November 1. After November 1, you can get a self-issue permit.
It's unbelievable how many people visit these trails. Last year I was unable to get a permit, however, the year before I did; spent five days on the mountain. I'm hoping my luck will be good this year.
When I first reached the summit of Whitney, about 20 years ago, it was much easier to get a permit - no lottery.