I have items that use a reference to potions to get mob effects and a machine to make them.
I can't simply use a potion as an input for the recipe since the player doesn't directly interact with potions but potion items.
I can get the registry location for the potion easily enough.  How do I get a reference to the actual potion item to set an an input for the recipe?

Why not just use the BrewingRecipeRegistry and hook it through there if this is performing the same task as a normal brewing stand? If not, that should still tell you how to do brewing checks and transforms.

Looking at brewing did help.
I believe that I have figured it out.
The approach that I am taking is to use the potion itself as an ingredient in my recipes from my provider and let my machine block do all of the vetting and massaging.
The player would be putting a stack into the slot.  Since the actual potion information is held in the stack's tags, my block would look there to determine if it holds a potion and what kind of potion it is before selecting the appropriate recipe.  For actual processing, it passes the potion to the recipe.
I still have to work out the new UI, but I am confident that this approach will work.
Here is one recipe.