According to the output of the "proj -lP" command:
gnom : Gnomonic
Azi, Sph.
gnomonic projection can only be used with a spherical earth model. So you
are going to get undefined behaviour / errors if re-projecting between an
ellipsoid and a sphere.
Unfortunately I don't know enough to be able to explain it any better than
that.
One last thing you could try to get the results you want would be to add the
line
towgs84: 0,0,0
to both the PROJ_INFO files for your two locations you are re-projecting
from/to, before running v.proj. It might fool PROJ into doing some extra
ellipsoid/sphere conversions; I don't know.
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