Have you tried legs out in the Moby? There's no reason at 5 weeks he has to have his legs froggied inside the carrier; try the hug hold with the cummerbund over his body but his legs out the bottom so they're free. Just make sure to spread each side from the back of his knee to the back of his neck so that his body is fully supported. Rotate his hips towards you so that he's sitting on his bum and thighs rather than dangling.
If that doesn't work out, then I'd recommend a buckle carrier or a mei tai with an adjustable base that can be narrowed so he can ride legs out. Buckle carriers that would probably work would be the Pikkolo, Connecta, and Beco, and mei tais with an adjustable base include CatBird Baby and Silly Goose.