I want to purchase a flight from Bangkok (BKK) to San Francisco.

For the 72 hour free transit, you are only allowed to stop in one Chinese city, but according to your travel route, you will stop in two, so the 72 hour free transit is not applicable.
But if your total layover time in Guangzhou and Wuhan is less than 24 hours, the entry permit is not needed either because you can utilize the 24 hour direct transit.
Otherwise, a transit G type or tourist L type is required.