Transit via Hong Kong both directions

No, this is not possible for any type of visa free transit scheme because it is considered as a round trip.

The very basic rule of 72/144 hour visa free transit is that the immediate points before and after of your mainland Chinese destination have to be in two different countries or eligible territories (eligible territories are Hong Kong. Taiwan and Macau). As you can see both your both immediate points are located in Hong Kong. If you proceed with this itinerary you will need a Chinese visa obtained in advance.

I suggest you to slightly alter your flight plan if you can. So, you can fly to Beijing exactly as you have described. When returning, you will not take a flight to Hong Kong, but a direct flight to Macau. Like this you will have two immediate points in two different countries/eligible territories and no visa is needed. Since Macau is so close to Hong Kong, you will just take the first ferry or bus or whatever to reach Hong Kong upon your landing in Macau.

By the way, it is 72, but 144 hour visa free transit in Beijing.