The untilted version displayed here wasn’t proposed by Raisz (as far as I know).
Interestingly, a projection that matches the untilted Raisz Half-ellipsoidal was proposed by Michael Ossipoff using the name Orthographic-Aitoff, and developed (but never published) by daan Strebe, labelled pseudorthographic. See mapthematics forum.
Jump to different depiction of this projection:
Specified in [square brackets]: Actual size of the projection
(minus the black or white background). When marked with [≈], sizes with and without
background are approx. the same.