I have tried to follow your topic before. But it seems above me.

At least one Canadian bank has created a mortgage contract for non-usury Muslims. Basically the bank has title of the house, and the "owner" pays the bank rent. At the end of the specified period, the bank turns the house to the owner. If the owner decides to "sell" beforehand, there is a provision in the contract how the disbursements will be divided between the bank and the owner.

I'm pretty sure the bank gets the same (or better) interest revenue from this mortgage contract. And the Muslim can say he didn't pay any interest because he was a renter. But this is just some sleight-of-hand to me.