I'm aware that you want as little headspace in your secondary as possible. As, any oxygen will just aerate the beer. There was about 3 inches of trub at the bottom,
I sampled it (pumpkin ale) after transferring it to secondary - and it tasted strongly of alcohol.
Hydrometer reading was consistent at 1.020 for a few days.
Should I possibly add water? Bad idea?
Adding water has the potential to do far more harm that letting your beer sit as it is. Aside from that, you likely had CO2 outgas from your beer while you racked it and it probably filled most of the headspace anyway.