Do lay overs count as a stop?

Every stop (landing) is considered in the same way, so you really cannot take a flight to Chongqing from some other mainland Chinese airport and remain eligible for 72/144 hour visa free transit.

You idea to use Hong Kong is fine, but you have to know that you are not allowed to return to Hong Kong as you have planned. Anyway, you can return from Chongqing to Macau by direct flight and after that take a bus or ferry to Hong Kong. So, your entire itinerary will be:

Canada - Hong Kong - Chongqing - Macau - Hong Kong

You can also do this, if you find a cheaper ticket:

Canada - Beijing/Shanghai - Hong Kong - Chongqing - Macau - Hong Kong

Also, you can think about this option that is probably even more logical:

Canada - Tokyo or Osaka or Seoul - Chongqing - Hong Kong

This last option has the least number of flights and hassle and the itinerary is logical geography wise.

As you have seen, I have intentionally written 72/144 hour visa free transit because of the announcements that Chongqing will become eligible for 144 hour visa free transit starting from December 1 of this year.

thank you for your response! I do have a follow up question if you don't mind... Would the trip be valid from Hong Kong > Chongqing > Taiwan? I am not sure if Hong Kong, Macau, and Taiwan are considered as individival regions. From Taiwan, I can stay for a day to see a friend and then fly back to Hong Kong. Thanks again!

An itinerary:

Hong Kong - Chongqing - Taiwan

Is definitely eligible because Hong Kong, Taiwan and Macau, although a territories and not countries, are considered as separate countries for visa free transit purposes. In other words, you can use exactly such an itinerary and be eligible for 72/144 hour visa free transit in Chongqing area.

Just one warning... Your flights to and from Chongqing have to be nonstop.

After you have reached Taiwan, you can stay there as much as you want and from Taiwan you can take a plane to Hong Kong without any problem.