I think it would be better to use a larger diameter outer support tube around the helix acting as a radome.
The helix reflector plate could probably be made a bit smaller, but it didn't seem to degrade the RX S/N by any appreciable amount, so I didn't bother chopping it down. I used PCB because I had it to hand, but aluminium, brass or whatever would be OK.
The underside of the 1/4 wave impedance matching line one the first turn of the helix has got self adhesive Mylar foil on it so that it doesn't short against the body of the N connector, when it is bent close to the reflector in order to achieve the best Return Loss.