Francis,
Consider this idea: When you go into the Visitor Center S of Lone Pine to pick up your permits, check on the Whitney Main Trail permits. I'll bet there will be dozens available, because the weather forecast will cause at least half the permit holders to bail. Ask them to check for entry on the current day you're there AND the next day.
If I were making your plans, I'd make the longer route you're planning to be Plan B, with Plan A to pick up the Main Trail permits. (There's currently one overnight Main Trail permit available online
for Tu, Oct 2.)
If the Main Trail Plan A works... Take it slow and easy, hiking no farther than Outpost Camp first day, maybe even Lone Pine Lake on Day 0. Then maybe Trail Camp on Day 1 (or just Outpost Camp if you actually start on Day 1.) Day 2 could move to Trail Camp. Day 3, from Trail Camp to summit and back out. This sure beats packing camping gear up and over from the west side. This plan gives you a much simpler escape route if the storm is too bad to proceed. I'd hate to be stuck on the west side in the face of a storm, with a major climb up and over Trail Crest as the only exit. If the trail is ok to hike above Trail Camp, when you are there, then you can proceed. If not, you have a quick and easy exit.
On the other hand, if you are over Old Army or New Army or Cottonwood Pass, you have a long hike out, and with your car parked at Horseshoe Meadows, you might have a blanket of snow on the road for driving out. My plan A means you don't need to worry about a shuttle, since your first plan would require shuttling to the trail head before the hike, or somehow getting up to get your car from HM after the hike.
Good luck!!! and please report back how it goes.