The answer seems to be to use a resonant antenna for each band of interest. One of my neighbors, G0RPM, has had good results with a parallel dipole made by Alpha Delta. I called the UK importer Martin Lynch to enquire about these and was told by an unhelpful person they were out of stock and didn’t know when they would get any more in. As a result I have decided to stop being lazy and build one!
The plan is to have an antenna for the 80-10m contest bands. This means four dipoles, 80m, 40m (which also works on 15m), 20m and 10m which I measured out in my hall from wire I had knocking about in my store.