The city marked the property for demo notice.

the question you need to ask yourself on any insurance, is what would you do in a total loss, if not replacing it, demoing the building and selling or donating the lot is ok for you then go with the cheaper, if you would want to rebuild then it may be worth the extra. 

I would have been much better off hiring a demo crew, lesson learned.

You could find somebody pretty cheap to demo it in 1-2 days (not that much money); than you could put down whatever you wish.

A contractor I use was telling me about an electrical job he did where he bid to demo all knob and tube and run new electric on a high end flip.

You should also be able to ask for a mini demo and have them work through a few accounting tasks so you can see the similarities or differences.

After closing there was two weeks of demo and then a planned quick turnover for another place.  

Removed walls in living room to make it more open concept ~$2.5k (we did demo)4.

General contractors, demo teams ... shoot me a line.

I will still do a deposit I sometimes will do demo first in order to get it.