have you tried your Kociemba's algorithm programs for the composition of Pons Asinorum with superflip?
after superflip, this is probably the second most likely candidate
for an antipode. there are only 4 positions which are fixed by
all 48 symmetries of the cube. they are:
pons asinorum, and
the composition of superflip and pons asinorum.
obviously start is of no interest and neither is pons asinorum.
my quarter turn version found this in less than one minute:
B3 L1 D1 L1 F3 U3 D3 L1 B3 D3 F3 R1 L3 F3 U1 D1 L2 U1 D1 B2 22q, 20f
so this position is at least as close to start as superflip.
i've tested (but not yet extensively) all the local maxima given by
hoey and saxe. i'll give a report on these some time soon.