Phil wrote:
"If not, what other homebrew antenna will be fine for the purpose?"

I believe Walter Maxwell, W2DU, while working with RCA`s satellite
program, designed quadrafilar helix antennas to communicate with the
birds. Look at their pattern on page 765 of Kraus` 3rd edition of
"Antennas", then compare with patterns shown on pages 763 and 764. The
advantage is clear.

Best regards, Richard Harrison, KB5WZI