Thank you for all the replies, a solid consensus for winging it, so that is what we shall do; except the first and maybe last nights in Europe. I will ride down to somewhere near Cochem on the first night, perhaps not Cochem itself as we stayed there a couple of years ago.
Haven't stayed in Cochem (there seems to be a price premium to stay in the town itself) but have stayed just upstream (Ernst) and downstream (Klotten). A pleasant hour's walk along the river from Ernst to Cochem, or catch the bus free (never really got to the bottom of the reason but seemes to be something to encourage tourists onto public transport). But every town along the way has lots of hotels at all sorts of prices.
Trier is indeed a nice city. We stayed a few years ago right opposite the Porta Negra. Most of the restaurants stop taking orders by 8pm though!