While all posts so far have been on point, let me add another thought - you're recording, not playing live; this isn't an "either or" situation, as you can easily have both. Record a couple "thick, wet, and dreamy" tracks with the levels of saturation you want (maybe try a hair less gain than you're using, though) to give the "sound" of guitars so distorted they're washing out, and then over that overdub another pair of tracks that are cleaner. Use the cleaner tracks for definition and note clarity, and the heavily distorted tracks to give it that super-saturated, washed out sense. It'll take a bit of juggling, getting the relative levels between the two right (and you might need to add a fair amount of compression to the cleaner tracks), and more likely than not you'll want to differentiate them further with EQ, the cleaner one being pretty bright and the gainier one being dark and middier, would be my starting point, but since you're recording, you really CAN have it both ways.
"They can kill you, but the legalities of eating you are a little dicier." - David Foster Wallace (1962-2008)