I spoke with our inspector Bill Case yesterday, and have a much better understanding of the permitting process.
Once the water disconnect and asbestos removal is done, we can get a demolition permit any time, "over the counter". So we could do this anytime after Saturday.
Getting the building permit, however, might take 2 weeks, for zoning review and drainage review. We need to get that application in ASAP, but it doesn't have to be granted for demolition to proceed.
The ideal setup is to have the building permit filed early, so that excavation can proceed as soon as demolition is certified complete, while the machine is still on-site.