You could probably get by with a type of genio that is in the out and down direction. It is not a 'sliding' genio that slides out and up. The type I'm talking about is sometimes called 'oblique' genio where a hard material like a slice of medpore block is sandwiched between the bone cuts. It allows the type of out and down diagonal direction where there is both advancement and some elongation to chin. It will not make the under lip chin fold deeper. But you need to find a doc that more genio combinations than just the 'sliding' genio.
Ya, I see the lower jaw is recessed. But not so much that you couldn't mask some of it with the type of genio I suggest. Even when only the lower jaw looks recessed, they often have to do the bimax so the bite fits together. However, IF someone could do a SINGLE (lower) jaw only (Diagnostics needed to even find out), that would be ideal.