Try a two-way radio or cb shop. The old extra large whip antennas, like the one on Andy Taylor’s police car in Mayberry, employed a large hole through the body panel. A similarly large rubber plug is available to stopper this hole when the antenna is un-installed.
Your patch theory seems sound, as well. A well-applied repair always adds an air of TLC, in my opinion. After all, anyone can pay to have the panel replaced, but not all have the energy or craft to repair for themselves.
Jeff & Cindy
'09 27FB Flying Cloud
'91 350 LE MH