POL fitting on a propane regulator -> pipe: what do I need / will it work?
Simply changing pipe size does not affect pressure. Flow affects pressure: for a given pipe size, pressure drop increases as flow rate increases. Likewise, for a given flow rate, pressure drop increases as pipe size decreases. We can't say anything at all about the pressure drops that might occur in your system without knowing a lot more about the flow rate, ie the consumption by the gas appliance.

My first reaction is that the whole project has the suspicious feeling of being built on some false premise. I feel this way because gas appliances typically require an inlet pressure around 11 inches water column (about 0.4 PSI). It strikes me as "wrong" to have plumbing bringing gas into a building at 20 PSI.

As to the shopping part of the question: it looks like you've chosen a part that matches your description, but the vendor might be in a better position to confirm that.

As to whether the adjustable regulator can work with just 20 PSI on the input rather than full tank pressure: charts of Propane vapor pressure on Engineering Toolbox indicate that propane's vapor pressure at 0 degrees F is about 40 psia, which is about 25 PSI gauge pressure. If that regulator works when the propane is very cold, either because of winter weather or because of prolonged use, there may be reason to expect it'll work in the setup you described.