I have the good fortune to be able to fire a wood burning kiln a few times a year. We make cone 10-12 in the span of a day. Like has been wisely mentioned previously in the thread, just because it's not anagama, it doesn't mean it's not legitimate woodfiring. The design of this kiln is called the Phoenix Kiln, named for the Phoenix Workshops of Dunbarton, NH in the late 70s. There's an old issue of the Studio Potter (Vol 7 No 2) that describes it, and it's also discussed in the book Wood-fired Ceramics: Contemporary Practices. It's a small spring arch cross draft that climbs quickly. The placement of the firebox beneath the ware chamber is key. As the flame travels beneath the ware chamber it heats the floor of this section, gaining ambient heat before the flame comes into direct contact with the ware. Also, unlike in an anagama or norigama, there is no struggling with the cool ground. The pots are up off the ground so the pots and chamber heat very evenly.
We use rough ends from the lumber mill that we purchase by the bundle and cut down to the right lengths. We use about a three quarters of a cord to a cord and a quarter per firing depending on how long the wood's been drying, how tight the load is, etc. Admittedly there is not the level of ash buildup you'd see in a more traditional 2 or 3 or 4 day firing, so we also salt at cone 10 to supplement. We get great results.
The kiln was built in southern Vermont about 10 or 12 years ago, and after being relocated a number of times via crane and flatbed truck, the kiln's owner had the genius/insane idea to put the kiln on a trailer. So for the last few years it has been on a 20' heavy duty trailer. The kiln and trailer weigh about 10 tons total. With about a week's notice (and a large enough truck to haul it) we can take down the flue, support the arch with a form and drive to somewhere new to set it back up to demo or workshop. It's an ordeal to move, but pretty straightforward. The last time we moved the kiln was to it's current home in Burlington, Vermont's south end where the kiln's owner and I run a weekend workshop a couple times a year.
As you look to faster woodfiring methods, check out the Phoenix Kiln. It might be a good fit for what you're looking for.