This hurts regular people far worse than the upper class

As it needs to be, of course. Only regular people are a large enough group to create an inflationary environment. One rich guy with an unlimited bank account faces no competition to drive prices higher.

Which is the challenge the BoC faces. Interest rates don't impact the poor, at least not directly. They aren't given loans, so rates mean nothing to them. Rates can only try to scare the small number of rich people away from employing the poor, but the rich can shoulder rate hikes for quite a long time before they give up on employing the poor.

Property taxes should increase exponentially with each additional property you own.

Same problem, though, as only the rich own property. You need something that targets regular people if you want fast results. As before, trying to squeeze the rich might work eventually, but they can hang on for quite a while. Higher income taxes across the board would curb things pretty quickly, though.