Three points worth pondering:
A SETI Institute engineers chose saw tooth LPAs for an upgrade to each of the 42 dishes in their
Allen Telescope Array;
B Engineers the world over (citing budget concerns) have decided upon trapezoidal LPAs
for the 100-plus dish SKA project;
C Nowhere, it seems, do radio-telescope engineers choose a dipole LPA for the all-important sensor
element of a radio-telescope.
Whatever the advantages up in the GHz range, ought those not to scale (down in f, up in size) similarly for use at HF? It's a question, anyhow, itching away in the back of my mind. Worth spending a little computer time on, at the very least.