USA citizens travel from Hong Kong to Shenzhen and to Zhongshan/Guangzhou for multiple day-trips

You cannot use 24 or 144 hour visa free transit for such a purpose because a transit implies the existence of a third country or eligible region (eligible regions are Hong Kong, Taiwan and Macau) or to be precise, the immediate points before and after your mainland Chinese stop (destination) have to be in two different countries or eligible territories.

In other words, an itinerary

Hong Kong - any mainland Chinese point - Hong Kong

Is not a transit, but a return trip.

You need something like this:

Hong Kong - Guangdong province (by ferry or air only) - Macau (by ferry)

As you can see, you can take a ferry from Hong Kong to Shenzhen (Shekou port) or to Nansha port located south from Guangzhou. Before your departure from Hong Kong you will have to buy a ferry ticket from Shenzhen (Shekou port) to Macau and have it at hand, ready to be presented to both Hong Kong and to the mainland Chinese authorities as a proof that you will be in a real transit. Also, you will really have to take exactly that ferry you have bought your ticket for.

Only the suggested itinerary will allow you to enjoy 144 hour visa free transit that is valid for the entire Guangdong province, but please keep in mind that your stay in Guangdong province has to be longer than 24 hours by just one minute based on your scheduled ferry arrival/departure times. So, having a stay in Guangdong province just slights longer than 24 hours is essential!

Alternatively, you can depart from Macau by ferry to Shekou port in Shenzhen and then return to Hong Kong by high speed train to Hong Kong from Shenzhen or Guangzhou stations directly to Hong Kong West Kowloon station. Having a train ticket before your departure from Macau is essential as well as your more than 24 hours stay in Guangdong province.