Hi Dennis,
You're seeing a lot of Dryness and Yin deficiency symptoms, there. The cough occurs during the Jue Yin time of day. Jue Yin organs (like the Liver and Pericardium) rely on adequate Blood to perform their function of spreading (and descending) the Qi. So you need a Blood or Yin tonic that descends Lung Qi.
I guess the first thing I'd wonder about, then, is Xue Fu Zhu Yu Tang, which has Blood moving properties as well, but has the overall right direction of action you need (downward); and a reputation for efficacy for chronic cough where there is Blood deficiency.
I'd go with that first. Bai Hu Gu Jin Tang (or Dry Airway from Natural Path) is another choice, but it is purely moistening, without the Qi moving attributes implied as necessary by the time of day when symptoms are worsening. So I'd try XFZYT first
Hope that helps!
Steve