Nothing wrong with your plan except a couple of things I would change.
A JD110 Tractor/Loader/Backhoe is NOT the right tool for that job. That model BH/Loader is cute as can be but they did have some problems....nothing JD couldn't have fixed or shouldn't have fixed...but they discontinued the very popular machine instead.
The machine you want is also by JD and is yellow, but it is a JD310/Case580/Cat316 of any vintage, not a 110. Those are the backhoe loader combo you see by the dozens on every construction site. Buy a good used one from your local utility company or school zone.
Start with the JD310. Most popular and best price...usually. Then Case580 if nice condx.
Second, for demo work the backhoe MUST have a thumb on it.
A skid steer competitive in price will not lift high enough dump far enough forward to fill a dumpster or commercial truck. It's what the JD310 was made to do.
Third, be sure to include the cost of either big dumpster roll-offs for trash.... or else hauling and dumping. It will be substantial. For a job here including 10 miles to the dump:
A standard JD 310 front loader bucket holds one (1) cubic yard of material. The green roll-offs that the truck drops off for you to fill with trash and broken lumber hold 12 cubic yards packed down hard. Here, they cost 600/700 apiece to drop off/pickup/dump. If you do it with a pickup truck instead, a PU bed will hold a bit less than 2 cubic yards and costs $100 to dump at the dump/trash site. A 12 foot trailer will hold 2 to 3 cubic yards heaped and tarped... and cost $125 to dump. I figure that house is going to be somewhere between 7 and 20 roll-offs demoed.
It all depends on how you stack the roll off... Using a helper with a contractors trash saw, plus the bigger 310 with a backhoe thumb and xtendahoe can save you $4/5K in disposal costs.
All that is assuming no hazardous material.
I'd say the bid you got is too high for the photos you show. See if someone else will do it for $20K. If so, let them. Be SURE to include concrete removal in costs.
rScotty