Dough Management - 2 fridge or freezer process?

We have been up and running for about 18 months. We are growing very nicely and have plans in about 1 year to open a second outlet. I am trying to reach a more consistent ‘days of fermentation’ before dough is used for consistent baking.

Our current dough process;

Fresh daily
Ferments in fridge at stable 2-4F (dedicated dough fridge and rarely opened)
Dough is ready in 48 hours. Can be used at 24hr but not as tasty, so we tend to over estimate usage to be safe
We use a Dough Press with heated upper plate and love it. A long stemmed dough docker is also used directly on a screen to eliminate any bubbling since our dough is partially cold even after pressing.
‘Blown’ dough is recycled at 15% of batch
Dough can last up to 5 days, but not ideal either since during bake the crust tends to rise too much.

So ideally we try and use 2-3 days after mixing.

I am thinking of ways to try and always using our dough in the 2-3 day cycle. Has anyone tried a 2 stage fridge temperature process?

Proposed Process;

We would mix and store for 2 days @ 2-4F
Then transfer to a colder fridge around 0F to allow it to last longer and minimize fermentation
Pull as needed daily

OR

We would mix and store for 2 days @ 2-4F
Then transfer to a freezer to stop fermentation
Pull as needed daily

Any insight of how our quality would be?

Are the temps in your post correct?

Apologies, I am in Canada and my temps are in celsius.

The 48 hr temp is 2-4C or 35-39F.

Then I thought to move to another fridge at 32F