you're probably strong enough to do a muscle up. i don't think you're logic completely works on the "power" method. if i'm grappling and somebody pulls a guard on me that i didn't know how to pass, i wouldn't just pick any other pass and power it as hard as possible to get through. when you try to overcompensate with power, you're just admitting that you don't know proper technique. the shitty thing though is that unlike grappling where you can move really slowly and fluidly to figure out the proper way to perform a move, the muscle up is very hard to do slowly and fluidly the first time.
honestly try starting from the knees or sitting several times. if you're having problems with the false grip, dont' start with arms fully extended. start on your knees, grab the rings with arms as straight as possible while still maintaining the integrity of the false grip. if you're arms can only go to 90 degrees while still maintaining the false grip, then fine. pull your knees off the floor, hang there for a second with your arms still bent, and then attempt.
i like the method scott sommer's uses a lot. i feel it makes the transition, the hardest part, much easier.
after trying all this stuff, the last thing that really taught me it was taking the rings out somewhere where i could do the MU from a full dead hang. in the gym, it's hard to find a spot at which you can hang the rings and start from full extension. starting from a full dead hang felt most natural as opposed to either keeping my leg curled hard back or in front to keep my feet from touching the ground. once you learn the form, you can do these ones close to the ground fine.