that's some research u have there... thanks a ton!! only issue with the sites you mention is that none of them open in English... gumtree included...any suggestions to circumvent that?
With oferty.net, click on "Mieszkania" on the first page.
On the search engine page enter the following:
Województwo Gminy / Dzielnice "mazowieckie"
Powiat / Miasto "Warszawa"
wszystkie = your choice of neighbourhood ("Śródmieście" = central Warsaw)
Rodzaj transakcji "wynajem" (type of transaction "rental")
Powierzchnia mieszkania od do (size of apartment, in square metres, from to )
Cena mieszkania od do PLN (price of apartment, in PLN, from to )
Liczba pokoi od do (number of rooms, from to )
Filtruj wg daty ciągu 7 dni w ciągu 30 dni zaktualizowane (filter by date advert was placed, within 7 days or within 30 days)
You can use this auto-translation page to get some idea of what the ad says: translatica.pl