I interpreted the post as doing only a section of the trail, and limiting the entire trip to 30 days. I was not clear if the $300 was extra cash after all backpack food were provided. If you had $300 for, say going to town every 5 days, it may suffice. And if you had family or friends take you to the start and pick you up there would be no transporation cost. If you were planning on buying backpack food (instead of having it already paid for and mailed to each spot) it would be tight. Good quality light weight backpack food can be pricy.

As for emergencies, I would just carry a credit card. It depends a lot on your "support team" at home. If something happened, can you just call them and they will come and pick you up?