I may be missing something here, but why not produce a
gain or field pattern for each antenna on the same
signal, random or otherwise and overlay each pattern
and put in memory? ( cheap laptop and use a loop antenna
for reference )

In one of the early antenna compendiums ( ARRLL)
a Peter Dobbs of the U.K. supplies all the info
and program to get you onboard quickly and inexpensively.
Art