I think everything you have said in your post is correct. I tow with different trailers regularly, and ride quality is severely compromised by over inflated tyres. They should be adjusted to the load being carried. That calculator you have found seems a good source to use. The worst trailer I have is an ifor williams with low profile tyres (to reduce the loading height), and even though it has suspension, it has a high load capacity, so the tyre pressures are high, and when towed with no load on it jars and bounces over every lump in the road.
Alastair