What kind of tax diagram can show the full consumer tax burden?
I would recommend that you read what Harvey S. Rosen and Ted Gayer have to say about taxation and tax burdens on their book, Public Finance.
Your hypotheses for perfectly inelastic demand might be flawed, to the extent that (1) the house market is competing with Airbnb-type companies and (2) -for inelastic supply- there is an affluence in housing available (that is, there are vacant houses -which is most always true in most first-world countries).