My guess is your problem is that distance and azimuth are in the wrong order. At least if I calculate the endpoint from travelling 90 m along an azimuth of 111,321° == 81°, I get approximately the same result you obtain above.
It may be useful to you to note that GeographicLib.jl provides a Julia implementation of Charles Karney’s algorithm (used by Proj), although it is an unregistered package.
The contents of GeographicLib.jl will be folded into Geodesics.jl fairly soon and then the latter will be registered.