Would the following be eligible

That can work without a pre-arrival visa, but for Shenzhen, you have to get a VOA which is not valid in Shanghai and costs the same as a 10-year visa if applying in the US . You would first get the VOA at the border and enter Mainland China from Shenzhen, then leave Mainland China from Shenzhen for Hong Kong and fly from Hong Kong to enter Mainland China again in Shanghai, and use visa-free transit in Shanghai. Not having a visa prior to arrival means you will be spending a considerable amount of time at border control. Flying directly from Shenzhen to Shanghai is also not permitted without a pre-arrival visa.

Americans are not eligible for VOA in Shenzhen (plus cant leave the city). Getting a 10 year multi entry visa as an American is the best idea. Just make sure you have more than 1 year left in passport or they may only approve for the 1 year. Of course once passport expires you will have to travel with both passports on you as the Visa is still good past passport expiration.

Not true. Americans are eligible for Shenzhen VOA since around late 2016 or early 2017. Although the 10-year visa is the more efficient and economic option here.