I don't understand how the "glue the center section first" suggestions are going to work. How do you keep things aligned and square while gluing an H shaped object (if I am correct about what's being proposed?) Seems like the side rails are what keeps everything square. There are only the six joints to apply glue to, you just need to male sure you don't get any into the grooves for the panels so they can float free in the frame.
Just practice your glue up dry a couple of times, paying attention to where you put down the clamping blocks so you actually have them in place when you need them. I think you'll find it not so hard in practice. Just work out a sequence that works for you.