I am not expert for sensitive circuits, however I am not exactly sure what does it mean "noisy ground plane" - actually I think I know where this is coming from, I am just not sure if that is how it works. After doing a lot of videos with Eric and Rick, I would say, understanding return currents could be the key in this case.
If the power supply board (the first one) is designed properly, I am not sure if we can say it's ground plane is going to be noisy. If the whole GND plane would be noisy, there may be something wrong with the design. In my opinion, all the "noise" should be local in the critical places of components and layout. I do not think it should spread through the whole GND plane .... if it does, it would mean the return current path is not controlled properly .... but I may be wrong.
I guess, this is not really answering your question, but I hope it will help to have a look at this system through a different point of view - how the return currents will flow.
These videos may help:
What Every PCB Designer Should Know - Return Current Path (with Eric Bogatin) https://youtu.be/icRzEZF3eZo
Ground in PCB Layout - Separate or Not Separate? (with Rick Hartley) https://youtu.be/vALt6Sd9vlY