CWB - I've done several all-wood cooks on my Outlaw and they work fine. You do go through wood faster than charcoal, so you'll have to babysit the fire more often. In addition, you'll get a much smokier end product, but that's not necessarily a bad thing.
Here's an idea: start it with wood, and then add charcoal later in the cook. Once the fire is established, the charcoal will catch normally and burn longer. This may even out the temperature spikes a bit and it will definitely cut down on oversmoking the meat too.
If the issue is just with starting the charcoal and not with continuous burning, try blasting the chimney with a propane weed torch for a few minutes. I fire mine straight down the top of the chimney and my charcoal is lit and burning fiercely in a few minutes and then there's no problem.
I've also put a chimney on my old Coleman campstove for 3 minutes and gotten similar results, as well as on one of those big butane stoves with the side tank (which takes the long bottles, not the backpacking canisters). This isn't a trick for the faint of heart as it needs to be monitored closely. This also can't be done with stoves with the fuel tank directly under the burner as the heat will ignite the tank and send the stove into orbit.
Unlike propane, you'll never wake up scorched and naked in another county because you mishandled a bag of briquettes.