I think if you are expecting to go from 14 mph to 20mph just with a new bike with better wheels and tyres, you might be a bit disappointed. On one of my regular runs I have been averaging 15 to 16 mph on my winter bike. Yesterday I was on my old best bike with deep carbon rims and better tyres and I averaged 17.8 mph.
In the post you quote I did say an extra couple of mph improvement from 14mph over said distance, which you say I won't achieve. Then state that you do achieve the same improvement with the upgrades I suggested 😂
It's by the by how I perform, I was just hoping for some advice on buying a nice bike