The Bike carriers (Two kinds one mounts under a ball of a ball hitch, one you described) do not extend the hitch at all. ANYTHING that extends the hitch, including extension devices, drop (riser) hitches and so on will reduce the hitch's capacity.
What is a 5,000 pound hitch with no extension can quickly become a 4,000, 3,000 or even 1,000 hitch when you drop, raise, or extend the hitch.
That said.. I'd use like a 1 foot rise/straight through hitch and put a standard cargo carrier on the upper hitch.
Home is where I park it!