Screw-glue MDF shelf together, how to make it perpendicular?

[Alko]

I'm working on a bookshelf for the slanted ceiling, 2.50m high, 2m wide, in three vertical sections that are screwed together during assembly. Then moldings to cover around and between the sections. The material is 16mm MDF, 4mm plywood as the back panel. See SketchUp image below.

Now I have cut and painted everything, shelves, sides, and "top."

I plan to use 3+3 screws in each shelf, through the outside of the sides. Got some good Spax MDF screws. Also gluing (left unpainted where I'll glue, of course). But I'm wondering if it will be difficult to get it perpendicular?

I've made boxes before, where I measure the diagonals to ensure it doesn't become a rhombus. The same method can be used here, despite the angle, just draw a line on the front side of the longer side, at the same level as the shorter side, so I can measure the diagonals as if I had a rectangle.

But with the large dimensions here, it will be hard to press together if it's not the right angle, like you can with a smaller box. Also, there are many shelves, is it even possible to adjust if needed and before the glue dries, without giant clamps?

Maybe these are exaggerated concerns, but I'd appreciate any advice!

 

[z_bumbi]

Attach support with clamps so that the shelves are in the right place.

 

[Alko]

Other things got in the way as usual, but now it's finally time to glue and screw the parts together for the three shelf sections. Cut back panels in plywood that should work as a template to keep it straight, so the shelf doesn’t turn into a rhombus.

Initially, I thought about gluing and screwing the shelves to one side panel first at "exactly" 90 degrees and letting it dry before attaching the other side panel at leisure. But now I'm considering whether it might actually be harder to adjust and keep it straight when the glue has already dried on one side. It requires the shelf-side panel to be exactly perpendicular. Maybe it’s better to glue everything together at once, allowing for some adjustment/pressure using the back panel as a "template" before the glue dries?