my advice is you need to be able to handle paying a higher rent at a more touristy accommodation for a few months, and bargains appear on https://idealista.pt and usually won't be on there for more than a week if they are really low prices

or if you can swing it to stay somewhere cheap outside of lisbon or something and then catch an "internal" (no international flight tax) to madeira to go inspect it and just fucking take it if you can... having good portuguese may help...

probably it's a similar thing all over the place in europe these days

what i will say tho, is that rents in former yugoslavia except for slovenia are really much cheaper, and some really nice locations... put it this way, i rented an apartment under the table in Sarajevo for 6 months for 220 euro a month about 2 years ago, i doubt the price has gone up much... it was a shitty commieblock but it wasn't terrible and there was a bathtub and a convenience store just outside the door nearby the main building entrance