effort only to find out that a coat hanger does a better job than my antenna

Brian,

That's the way!
Use straightened coat hangers, I'd bet you would find it very difficult to prove a "proper" antenna was better.

73 Alan G4ZFQ

Since you are NOT transmitting, SWR really doesn't matter all that much. Why not use the tried and true method of a dipole cut for 54.310Mhz and the reflector 5% longer and director 5% shorter. The spacing set to .125 the wavelength on the director/reflector distance to driven element.