The problem is that if you raise real estate taxes on your residential owner-occupiers, a number of them becomes insolvent (because this tax is discounted in the market value).

If their mortgage goes underwater, it does not mean they are insolvent, if their other wealth increases. You cannot decide a household wealth only from the balance sheet of their mortgage.
And anyway, this is an issue of politics. That is a very poor starting point for seeking remedies. Politics must follow policy, not the other way around.

Inasmuch as taxes crowd out amortisations, they don't matter to demand. Taxes destroy money, amortisation destroys money - either way, the money is destroyed.

No. This is the central point. Property tax destroys economic rent. Labour tax destroys wealth. A whole different thing.

Inasmuch as taxes crowd out interest payments, you reduce banker income, which ceteris paribus reduces demand.

It is not ceteris paribus at all. When banker incomes are economic rent (created interest charges over existing wealth, like land, real estate, shares etc.) these "incomes" are the actual "the beef" that destroy demand. This is exactly what property tax helps to get rid of.