Can't find link/pics from rimfirecentral.com, but take a segment of a 3 piece cleaning rod, put .22 brush on it and bend base of brush 90 degrees. Then you can just put it in through the ejection port and scrub the chamber.
Ultimately drilling the receiver is the way to go, but even then you have to take it off the stock to clean the chamber. If you make a chamber brush it makes it super easy.