I found a solution to this but it is quite ugly! Basically, when you add content controls to a document, under the hood, they get a number assigned to them. By using that number with a value in JSON format, I was able to get this to work using the dynamicFileSchema field. To make this slightly less ugly, I first pointed the connector to the file that I wanted to work with, thus exposing the content control fields. Then, I copied the actual name of each content control into the value. Once you have done that, click on the ellipses and peek code. This will give you the output of the number mapped to the field name:

Then switch back to the dynamic location/library/file and use the numbers in your JSON:


This was not quite the answer I was hoping for but I guess it is better than modifying the flow in each environment and having to remap all your values. I have not yet tried this with image controls or repeating controls.
I hope this helps someone as I wasted a good bit of time trying to figure this out and was not finding any answers from the old google machine!
Happy Power Automating!