I have the older model Big Easy and I have modded it to add smoke.
I'm not sure how these newer ones work, but the inner drum is probably made of stainless steel and
should deal with th heat from a woodfire just fine.
For what it's worth, a big easy is basically an infrared cooker that produces amazingly juicy roasts and poultry.
Even with the model you have, smoking and grilling are not it's best features.
I have about 8 propane bottles, and I've never paid for a single one of them.
Grab any free one that comes available, no matter how old and trade you can trade it in at dozens of places.
If you dont want to use propane at all, consider posting it up for a trade.
Many smoker enthusiasts have multiple smokers and will be down for a trade.
A wood or charcoal fired offset smoker might be more your speed.