What model of shifters are they? Sounds like a trigger of some sort with the two levers comment, but nice to know what specifically you've got. Assuming they're triggers, by cleaning them, did you spray liberal amounts of something with a fair amount of solvent like WD40 into the mechanism and work the levers while you did so? You don't have to take them apart literally, that may lead you to never getting them back together, just use the same access as the cable uses.