Is the issue that you need to up your budget or that other people on the same budget are getting the property first? I've no idea whether this will work but if I were in a similar position I'd go to a couple of local letting agents and offer them a finders fee for getting you to see it first (and on condition you take it). Also be prepared to drop everything and view it within a few hours.
While one view on this is that you shouldn't need to pay this "bribe" (and I agree), the other view is that you are employing an expert in the area to source a property for you.