They could always take some liberties with the rogues.
Arrow has been using folks like Bronze Tiger & Deadshot, with Amanda Waller and Ra's Al Ghul coming up. Not your typical Green Arrow villains.
Moon Knight could borrow from Captain America's and Daredevil's rogues galleries. Typhoid Mary, Scourge, Batroc and his crew, Lady Bullseye could all work.
My main concern with a Moon Knight show, however, would be getting folks to realize he's not "white Batman".
Agreed. I would go you better and have characters like Slaymaster, Jigsaw, Deacon Frost, Kirigi, the Reapers, the Pride, Ghost, Crossbones, Flag Smasher and so show up as villains. I would also have Daredevil, Elektra, Blade, Punisher, Hannibal King, Werewolf By Night and Ghost Rider appear at some point. Another good idea would have Marc Spector start out as a SHIELD agent but decided to quit to go out on his own and resurface in the SHIELD series as Moon Knight later on.
And as for the last point, I do agree that has always been MK and similar Batman-lite characters' problems as they're always in his shadow. The way I see this working is to show that even though MK is similar to Batman, that he's more of a homeage than a ripoff.