Actually a 'Royal Mumak' would be pretty cool imo.
It should be larger than "normal" mumakil (though not by an excessive amount) because the Royal Mumak would be an older animal, tested in battle many times and even revered by the Haradrim, a kind of an "alpha bull" among its peers.
It still wouldn't wear actual armour but its age and battle experience would mean it has thicker skin than other mumakil. It would be adorned with "tatoos"/war paint in lavish colours and perhaps some 'persian carpet' style decorations probably with a red/gold colour theme.
The tusks could be steel reinforced and perhaps laced with gold while the enlarged tower would carry archers drafted from the Serpent Guard.
It would have the "inspires nearby troops" ability since it would represent the power of Haradrian Kings/Chiefs and simply because it'd be an awe-inspiring sight. It'd have increased morale since its experience would allow it to remain calm in battle more easily. It might even have the 'run amok' trait removed to represent its immense discipline but that might be a bit too much.
Availability should be very limited, recruitable in only 1 or 2 towns with a very slow replenishment rate (kinda like the citadel guard). Once recruited it would represent a unique centerpiece of the Haradrian army.
It'd be an 'elegant' stretch of the lore imo. 