I want to make either a queen or king size Thinking Outside the Block quilt using QAYG. Does anyone have any idea as to what method of QAYG I should use? Or is this quilt not suitable to QAYG?

Not totally impossible but near impossible. It would require a lot and I mean a lot of planning before during and after the blocks were made. You might be able to do it but most likely would have to divide your design into standard units for easier assembly. I would have to draft the units on paper and follow them in constructing the units
in order to take advantage of the quilt as you go technique.