I think a tree shear would have problems if the oak is hard and dry. The saw will, too, but less chance of damaging something (ask me how I know.. LOL). While I love the Tree Terminator and the service from the manufacturer is awesome, I learned my lesson trying to cut hard, dry oak. It cuts part way and POP it'll jump off the holding wood and hard to control fall plus it can damage/twist blades. The slow speed of the say will pinch and cut while letting the tree fall to one side using what's left of hinge wood to help the fall.. (in theory) plus the saw sticks out a lot further than a shear and less chance of needing your ROPS to protect you from falling wood (i'd still have lexan working in and under dead wood).
As far as value of logs.. a fairly successful tree contractor told me that there is money in firewood if you don't have to handle it too much. Having firewood choppers, at least down here, is a mixed bag. You can get someone responsible but I really doubt they would have insurance or follow any safety rules. To me, that's more of a liability unless the trees were on the ground, the guys were supervised, etc. Better, in my humble opinion, to pay more for a quality cutter or two or three who will wear chaps and buck the wood when it's on a the ground. Of course, in TX chaps are pretty much only worn by the cowboys at the rodeo. LOL.
Seriously, a little planning and this is a really cool job. You get to make something go away that's a

hurting the property value, b

will only become bigger problem (when tree start to deteriorate, cutting is 100% more dangerous and gets more expensive/messy), and c

you will actually improve and make the property pretty again.
There will be some money in firewood logs.. possibly. Whether it's splitting on site in measured cords, stacking on pallets and wrapping (it's already dry and ready to burn next season), hauling the roundest/cut to equal lengths logs to a firewood processor and expecting to sell at deep discount, or finding a reputable cutter that will take the wood for free but cut down on your disposal.
You get enough gone/sold and it's starting to look more afforable to bring in the bigger mulcher, good skid steer mulcher operator for tops/stumps, or a tub or horizontal to take care of what's left.
The mulch can be used for remediation or sold at wholesale or deep discounts if a material yard is willing to send big dumps or live floor trailers to get the mulch.
I'm sorry for their loss.. Had to be a horribly frightening fire. I was a wildland firefighter in another life and I've been there when mother nature does her worst and leaves a big mess but from what I read about Possum Kingdom, that's one of the bad ones.