Thanks for your reply, Redrobes! Following that link I managed to create a custom CRS that actually works, by deleting the parameters "+datum=WGS84", "+rf=800", and replacing the +a and +b with +R, which is the radius of the custom ellipsoid. Then, in order to georeference the equirectangular map, I defined the four corners of the map this way:

Upper left: -180, 90
Lower left: -180, -90
Upper right: 180, 90
Lower right: 180, -90

The resulting CRS doesn't have a predefined datum but is more than enough for any worldbuilding shenanigans.

Just in case anyone has the same problem.