Oblique Cylindrical Equidistant to change planes

I’m working on a astronomy article and felt the need to show how things look when changing from horizontal coordinates to celestial coordinates and viceversa. A world map is very well suited for this purpose (there is no constallations background available).
Cylindrical equidistant is very simple and quite used nowadays, but the only oblique transformation I’ve found here is Oblique Mercator, so, I tried it.

Using the following code:
gmt coast -R120W/240E/-80/80 -JOA90E/0/50/20c -B15g15 -Di -A1000 -Wthinnest -Slightblue -png test50
(see attachment)

It’s not the goal I was pursuing because the second attachment is cylindrical equidistant and the meridian and parallel lines are “just similar”, regretfully cannot go form -90 to +90 with Mercator.

I’ve been unable with the Mercator Oblique to center the south pole in the middle of the figure (meridian 0) , where the plane inclination is max when looking south (180 azimuth) from a 40 degree location thus, a 50 degrees colatitude (both planes intersect on the E-W line, like in the second attachment). Will do a cut and paste if there is no coding solution.

Is it correct that there is no way to make an oblique transformation in Cylindrical equidistant? I guess it should be lot easier to perform the aforementioned task with it than with Mercator.

GMT is a wonderful program, congratulations.
Regards, Luis

mercator-oblique-50degrees.pdf (677.5 KB)
horizon-to-HA.pdf (864.8 KB)