Fly Into HGK, stay in Shenzhen and fly out of HGK

No, this is not an itinerary that can be used for 144 hour visa free transit. Having an itinerary:

Hong Kong - Shenzhen - Hong Kong

Means you will have a return journey and you will not be in a transit. Also, to be eligible for 144 hour visa free transit in Guangdong province, where Shenzhen is located among many other cities, the only eligible way is to enter it by air.

I would suggest you to use 5 days Shenzhen visa on arrival in your case. The best way is to take a ferry from Hong Kong to Shekou port in Shenzhen and to apply for a visa on arrival at Shekou visa office. You have to know two details in this regard. The opening hours of Shekou visa office are: 9:00 - 13:00 & 14:30 - 16:30 and the price of this visa for US citizens is quite steep due to reciprocity and here we talk about 1,295 CNY that can be payed by card only. After your stay in Shenzhen, you can return back to Hong Kong by taking any mean of transport, including a high speed train or by using any available border crossing. The company that offers ferry rides from Hong Kong to Shekou is CKS - Chu Kong Passenger Transport Company.