Is this route allowed 144 hr convenient visa?

NO, your itinerary is not eligible for the 144-hour visa-free transit as HK - Zhongshan - HK is a return journey, not transit.

A suggested itinerary for 144-hour visa-free transit:
In fact, you can fly from US to Guangzhou and then take a bus to Zhongshan. After that, take a ferry to HK and then you can fly to Japan...

Remember that, you have to book your ferry ticket to HK before departing from US.

As Linda has pointed out, a changes in your itinerary are necessary. However, maybe a following solution will be more acceptable in your case:

1. A flight from Hong Kong to Guangzhou because you become eligible for 144 hour visa free transit if you fly into Guangdong province
2. Stay and travel within the entire Guangdong province, Zhongshan included.
3. Take a ferry from Shekou port in Shenzhen to Macau by booking a ticket for this ferry in advance. Also, you have to print out that ticket and have it with you as a proof that you are really in transit. You have to take exactly that ferry you have bought the ticket for.

Like this your itinerary is:

Hong Kong - Guangdong province (mainland China) - Macau

This itinerary is eligible for 144 hour visa free transit. Also, Macau and Hong Kong are so close to each other that you can return to Hong Kong as soon as you reach Macau.