The private finance industry need not be involved.
Just have government allow taxes to be deferred until time of sale with interest pinned to the cost of borrowing for government. That already exists where I live for people over the age of 65. The government can still get the revenue for free via borrowing and the payback is more or less guaranteed.
This really seems like the most fair situation, if we don't want to a) let retired people stop contributing their fair share, b) kick old people out of their lifetime homes during their most vulnerable years.