No it is not the Black Watch, as she is said to be in the picture too - as a newly laid keel. However, rereading the text I think you are right, the two should be in slipways 2 and 3. And the big ship furthest to the left here I think must be the Thor Dahl vessel pictured in my posting titled "Stavangerfjord" in the Passenger ship category today. That bridge on the foredeck and the goalpost masts are rather distinctive.
You can have this picture greatly increased in size here: https://digitaltmuseum.no/011014269278/flyfoto-av-akers-mek-verksted-sommeren-1937-d-s-baden-b-n-471-det-siste
Click on the picture and the new one has an enlargement button on the upper left. And then maybe we can identify them all?
I looked for the Thor Dahl ship, and Google presented two pictures that but for the ship(s) being light hulled were much like her. Unfortunately they were from the Lardex site, and that seems to be down.
Here is a list of some Aker built ships with pictures, sad to say they are alphabetical instead of chronological, but should anyone care to try to identify the ships, it may still be of some help: https://www.sjohistorie.no/no/verft/97515/relatert-innhold