Some More Possibilities
Eric's suggestions are good ones and will probably address the problem you are having. However, there may be some more things you might want to check. It has been a very long time since I last worked on my rear brakes, so my suggestions may or may not apply. And you may have already addressed these.
Make sure that both shoes are the same distance from the center of the axle. The drum will be centered on the axle, but the shoes may not be, causing the interference. Also, after you have backed off the adjuster all the way, make sure that brake cylinder pistons have retracted all the way by squeezing both ends with channel locks, just in case the brake return springs are weak. (If they are, you might want to replace them now.)
Good Luck!