This is my understanding of the permit system based on preparation for a JMT trip that didn't happen (yet). Others might have different or better information.
General permit information:
You will need a permit. The permit will list your starting trailhead and first night's campsite but there is no special JMT designation on any permit. Even if you leave from Happy Isles/YV, your permit does not regulate where your subsequent campsites have to be. It does not matter if you cross Tioga road if you already have a permit (this is all within the Yosemite NP boundary). The more-difficult permits to get out of Tuolumne Meadows will be those with a first night in Lyell Canyon. Once you have a permit (from whichever TH you start at), you will not need another permit. You can leave the trail to re-supply and the permit is still good. Going SOBO, you do not need any special permit to summit Mt. Whitney either.
I do not know if you can start at the Murphy Creek TH and continue on the JMT, but you should send an email to the permit office stating clearly your intended route (Murphy Creek to Glen Aulin to Lyell Canyon). They should be able to provide information and I got email responses within a few days to every question I asked. There is a backpacker's campground at Tuolumne Meadows if you need one.
It is still possible for you to get a permit from either Happy Isles/Yosemite Valley or Tuolumne Meadows, especially if you are hiking solo. There are some "walk-up" permits available at both places, when the wilderness office opens in the morning. If you can get to the wilderness office a few hours before it opens, you have a very good chance of getting a permit. You can camp at the backpackers' campground in YV and have less than 2km easy walking on a path to the wilderness office. You need to get the permit on the day BEFORE you plan to start. You can then hang out in the valley for the day, where there is a grocery store and restaurants.
Finally, if you don't have it, the JMT book by Elizabeth Wenk (available at Amazon) is a great planning tool and lists most of the campsites along the JMT.