I also suffered with Creeping Charlie! At one point, two thirds of my lawn was taken over. I tried everything under the sun. I finally tried Spectracide Weed and Feed. I mixed a much stronger solution than the instructions said. Used a handheld sprayer and really wet the "lawn" down with no rain scheduled for the next few days. Killed the Charlie and he lawn came back stronger than ever. I still get some Charlie coming back every so often, so I pull out what I can and spot spray it along with other weeds as general maintenance.
Hope these help: