I also have an outdoor oven, although it is at a summer cabin and I do not get to use it nearly enough.
I have tried using fatwood to start my fires, and have come to believe that it is not a good alternative. The small twig-like pieces of the fatwood seem infused with a sticky oil (which I think occurs naturally). The fatwood burns well, but the oil, which is almost like a resin from pine, has a distinct, "sweet", odor to it, that I do not like and I think my hang around the oven (could be my imagination). As the wood burns, the oil "boils"† †out of the wood onto the oven floor, where it is tough to get rid of. I still have some stains on the porous tile from the oil.
I use the commercial firestarter bricks available at Home Depot and other stores without problem. They have no odor and burn nicely. I understand that Mugnaini ovens are shipped with a free box of these starters, which I take as at least some kind of endorsement as to safety.
Good luck with your oven. It is truly a romantic notion to have your own backyard oven, and just about every guy I have to the house for a pizza party falls in love.