If you're right that the 11th Circuit is overworked, then that point actually cuts against your argument: let's put more judges there where they need more help, and not the DC Circuit.
The system is, we have these seats, created by acts of Congress, which need to be filled. The President nominates candidates -- ideally candidates recommended by the Congressmen in the region, for regional appointments -- and the Senate vets them, and confirms or denies their appointment. The Republicans, however, aren't playing fair: they have been refusing to even allow votes on the candidates, even while admitting the candidates are qualified. Furthermore, they are not cooperating in the nomination process, refusing to recommend candidates to the President.
It's not fair, and everything after that is camouflage. If it was really a concern about the workload of the judiciary, and act of Congress could add or remove seats as necessary. But it isn't, and Congress isn't acting -- they are refusing to act, never in good faith and rarely at all.
As an aside, why do you say that the DC Circuit is "underworked" instead of saying that the 11th Circuit is "overworked"?