Hainan VOA from USA

Yes, but only in theory. In reality, there are two main obstacles. The first one is the fact that there are no direct flights between US and Hainan. The second and the most important is the fact that only a very limited number of airports outside mainland China, probably only Hong Kong, would allow you to board the plane based on your statement that you will rely on Hainan VOA when you land on Hainan.

In reality, the best option is, as I always recommend, to rely on Hainan 30 day visa free access because like this you will receive a kind of invitation from Chinese authorized institution and you will be allowed boarding anywhere in the world where a direct connections with Hainan are existent. Anyway, in any case, regardless whether you rely on Hainan VOA or Hainan 30 day visa free access, you cannot arrive on Hainan by flight from the rest of the mainland China. Your flight has to be from the outside! The only better aspect of Hainan VOA is the possibility to travel to a mainland China destination, like Chongqing, as you have already mentioned.

One detail more... If you are a US citizen, then your much better option is to obtain a Chinese 10 year multiple entry visa with base price that is practically identical with the price of Hainan VOA.