Alright, I have two scenarios, each with advantages and disadvantages.
As I look at the firepit, the thought occurred to me that any setup will be contingent on the lip of the firepit being completely heat proof. If the lip is painted, and heat will damage the finish, that means everything has to be built within the bowl, and I don't think that's feasible without drilling into/modifying the firepit. If, on the other hand, the lip is just a weathered finish/gun metal-ish patina to the steel, then we're good. But I just thought I'd point this out before we go any further. You might want to try burning a small piece of wood on the lip and see if any damage occurs.
Assuming the lip is flame proof, attached are my two proposed configurations (see below). Bear in mind, as you look at this diagram, neither has a ceiling. Both ovens have split firebrick (4.5" x 9" x 1.25") bases that are suspended by angle iron. I choose angle iron for expense. I don't know how much angle iron costs at Home Depot (probably not cheap), but, a lot of people have old metal bed frames lying around. If you don't have one or know of anyone who does, you might try Craigslist- either looking for ads, or posting a wanted ad of your own. You also might look into metal scrapyards and recyclers.
I'm basically covering up the whole grill, putting strategically placed bricks that can be slid out to add wood, and forcing the hot air through holes in the back of the baking chamber (which is not that different than the gap that JD had in his design).
The strength of the square version is the simplicity of the design and the lesser weight of fewer bricks. The disadvantage of the square version is that you have to take a round black stove pipe, http://www.pizzamaking.com/forum/index.php/topic,4753.msg196815.html#msg196815
unbend it so that it's almost completely flat, and then put perfect 90 deg. corners to form the walls. I think it can be done, although I've never done it myself.
The advantage of a round oven is the easier fabrication of the round stove pipe wall. The disadvantage is the greater number of bricks/greater weight and the fact that the wood adding areas involve irregular brick shapes. You can try to cut these shapes out of bricks or you can cast them out of perlcrete. Perlcrete isn't inherently costly, but it can be tricky finding small bags of concrete, which may drive the price up. Both designs have gaps that have to be covered in order to force the hot air up through the baking chamber, so you have to find some kind of heat proof covering anyway, so perhaps if you're using perlcrete for that, you can use perlcrete for the irregularly shaped wood adding areas.
What you cannot use for any covering is aluminum, as it very likely will melt. Steel baking pans (usually teflon coated) might work, but they could warp, and, if they do, the hot air will escape in the wrong place.
One thing to bear in mind is that the angle iron supports will leave 1/4" gaps between the rows of firebricks, so you can't bake on the bricks directly. You will need to put another layer of quarry tiles on top of the bricks as your baking surface.
If you wanted to bake on the firebricks directly a far more elegant setup would be place the bricks on 1/16" to 1/8" steel sheet and support that with only two pieces of angle iron (no gaps). You'd need a steel sheet under the hearth and one under the wood adding area, and while 1/8" is pretty inexpensive, the number of cuts would probably make it cost prohibitive.
The ceiling can be either firebricks with angle iron running perpendicularly to the angle iron below, or, again, a more elegant, lighter, yet more expensive option would be 1/8" steel. You might be able to get a 20" square piece of 1/8" steel sheet for $50, but I don't know how much you're willing spend.
You could, in theory, go with pelcrete walls and bag the black stove pipe, but I'd like to see you with a material that can emit some heat, even if it is just thin steel.
Both diagrams are to scale.