i'm with the asian/third world squat totally, but i feel the best way to go about it is to grease the grove with it. at least 5 times a day, get down and hold the squat for at least a minute. it should hardly take any effort. your goal is to just chill out down there. imagine talkin with your friends and then just drifting down into the third world squat. if you think you could get down comfortably and afterwards hold it so comfortably that your friends wouldn't even think twice about the fact that you're now squatting on the ground, then you're probably in good shape. (in all actuality, your friends are probably gonna wonder what the hell you're doing no matter what. you should probably get new friends, ones that will squat down with you)
i also like do a lot of toe balances and lunges. generally i will get down in a third world squat, chill out for a min, then bring one foot in so that my heel is both under my groind and off the ground. i'll then support my weight on this foot so that i can freely pull in the other foot and hit a toe balance. then i'll start walking around on the ground. one foot will take a long step while all my weight rests on a toe balanced leg. i'll transfer my weight between legs. throughout all this i will stop at third world squats an toe balances. if at any time your knee feels bad or wonky, you're probably not in a proper position on your joints. your knees should not feel pressure and especially no torque. if your ankle flexors get tired, you need to focus on pulling your heels towards your asscrack. people call this duck walking. it great for building stability in a low-level position.
my goal is to make the transition between heel support and forefoot support smooth. that way you can easily have the coordination switching between times when you need to be on your heels (for lifting) or balls of your feet (for fighting or what not).
a lot of this is balance and a lot of people seem to forget to emphasize this with stretching. your muscle may be able to relax enough to get into a position, but you gotta have the coordination and control to manipulate that muscle when you're in that exaggerated position. thus comes balance.