Of course the EFT will work with LOA effectively, but there's some catchas there. If you have the "Ask and It Is Given" book, I recommend doing the process #22. It's most effective process in moving up the emotional scale one step at a time. I don't recommend doing quantum leaps because it leads to downward spirals you have experienced. Also you can look for the "The Work" process by Byron Katie if you feel that EFT didn't work in some cases.
What you have experienced about the downward spiral, it's a classic experience of doing a quantum leap and falling again to old beliefs. You didn't release the resistance correctly in this case so that's why the old resistance brought you back to the square one.