The standard Avons are a sidecar tyre, and the Blockley is a car tyre. Both have a profile suited to a three wheeler for road use.
I suspect if you use a bike tyre, you'll wear out the middle in short order. A motor bike leans and changes angle so wears most of the tyre - a three wheeler won't, so will wear a narrow band. The reason that racers use them, I think, is that the rubber is softer, so more grip, and the shortish life is not a major problem.
If you are wearing out standard tyres a bit quickly, you'll wear out bike tyres a lot faster!
I could ask a racer, but I think I'm right.