Using acid worked nicely for me:
Safety warning********** use rubber gloves, goggles, etc and never let acid come into contact with you*****!
I had an overflow that kept threatening to back up and overflow my tank. I got tired of constantly cleaning the basket only to have the clog re-occur a few weeks later.
I made up water for a water change and went down to home depot to buy Muriatic acid (12 M or 36% hydrochloric acid) from the pool section. I stopped my return pump and let the overflow drain as far as it could. I took the hose that goes from the overflow into my sump and put it in a bucket. I zip tied two ziplock bags around the hose inside the bucket it to make it semi-sealed. I poured the muriatic acid into the overflow and wow did it start bubbling. Go really slow, let it bubble a bit and when it subsides add some more. I went a bit too fast and there was a lot of fizzing. You want to minimize this so none of the acid gets into your display.
Make sure that this solution makes it into the inside of your overflow stand pipe by adding acid and freshwater until your bags/ bucket start filling. Once the bubbling has stopped, you've dissolved your clog. Carefully cut a hole in your ziplock bags with scissors (using gloves and keeping your face away!) Really carefully empty the bucket into a drain (if you have chrome in your sink that you like, it's best to first neutralize any remaining acid in the bucket with baking soda). Then, return the bucket under your overflow and start your water change by adding water to the overflow. Empty the bucket underneath a few times and you should have washed out all residual acid.
Not for the faint of heart, but my overflow looks and works like it's brand new.