Does anyone with horrible credit had luck recently finding a nice apartment? How did you do it?

In the next three months I want to move my family from a small apartment to a town house, but I pretty much ruined my credit and only in the last two years finally began paying it all off. There's evidence of paid collections notices if that's helpful.

Issue is, most places want to screen my credit and waste my time and money rejecting me without any other considerations. I'm willing to pay extra if necessary. Does anyone have good advice for me?

EDIT: argh typo in title :(