Alternate JMT start points

the monument itself is a very narrow strip of land, but beyond it i believe the wilderness is governed by the Inyo NF. call either their Mammoth or Bishop offices and inquire. if they are not the correct agency, they should be able to tell you whom to contact.

It's pretty easy to start from Mammoth Village and pop over to the JMT, I think it's actually a rerouted section of the old trail. That way you can skip the whole Reds Meadow/Postpile debacle.
Another interesting start could the end of Florence lake if they still ferry you across.

As others have noted, Inyo NF manages the wilderness permits from the Devils Postpile/Reds Meadow area:

http://www.fs.fed.us/r5/inyo/recreation/wild/permitsres.shtml

If you have a specific date in mind, you should reserve a permit–the Devils Postpile area is popular and quotas can fill during peak season (summer/weekends). The website above has information on when permits can be reserved (generally, 6 months in advance). You can fax in a reservation request. You can also ask Inyo to have your permit held for you at a ranger station if you can't pick it up during their normal hours, as long as you're not going into Kings Canyon/Sequoia NP.

Heading north from Reds Meadow, you can take the "High Trail (PCT)", "JMT North", or the "River Trail"–all converge near Thousand Island Lake. Heading south, you'll want the "JMT/PCT South".

Note that if you plan on exiting via Whitney Portal, review the "Trail Crest (exit only)" information on the website–there's a separate quota to exit via the Main Whitney Trail. The challenge will of course be knowing which date you'll be exiting at Trail Crest, but I wouldn't expect any problems with the rangers if you make a good-faith estimate and are a day or two off.

Thanks to all, Those are some great ideas to look into.