Backing for the shelves has now been added back into the design.
My concerns about rigidity and Andy's comment that even a thin back will help, together with laying out the base and discovering how 'unflat' the back wall is - up to 1cm gap off the best straight line. It would look very messy if the shelves didn't have a back and I don't want to start scribing everything to fit the back wall so have thought about alternative assembly methods that will allow me to have a 6mm backboard to the shelves.
I haven't decided yet whether I will have just one fixed shelf (the bottom one) or none. If I find any twist in the verticals when I come to assembly then I will add a fixed shelf since the way I'm planning to sit the bottom of the verticals on dowels in the base may not be strong enough to correct it. The top is fixed to the verticals which extend into the void above the bookcase so confident of the fixing at this end.
New final assembly process (assumes the bottom shelf isn't fixed but easy to add in if necessary):
Start with the central module and fully assemble glue and screw the top from both sides, square and fit backboard. With assistance, lift and sit the verticals onto dowels in the base. Fix to wall in the void above top (not visible).
For the next module, dry screw the top into the next vertical. Fix the backing just along the new vertical edge (leave the top floating). Bring the side and top into position (again sitting the vertical on dowels in the base), clamp the top into position and adjust for square. Mark the exact position of the top on the backboard. Unclamp and remove from base, glue and screw the top edge, align the marks and fix top edge of back board. Lift the vertical into place on the base dowels, glue and clamp the other end of the top to the already assembled structure, and also glue the remaining vertical edge of the back board to the back of the previously assembled vertical (I see this as a tricky bit , not getting glue everywhere, might have to put some wedges in place first if the wall isn't flat along the glue line, ... unfortunately I cannot think of a better way of fixing this edge of the backboard to an already in-place and assembled module.).
The remaining modules just repeat this process.
Another major benefit is that there's no need to get the whole bookcase assembled in one big glue-up.