The fix

I've cut four new strips of MDF, and put two under each y-rail. All is re-assembled now.

I have also drilled all the holes in the y-stage, using as maximum the 4 mm drill bit and all the screws are in - all are 5 mm screws. I have drilled out the y-pivot arms, too.

Here is the diagram of the y-stage - the pivot arms are identical to the x- ones

The springs I've used are the 4.0 x 79.4 mm extension springs from the multipack, using 2 together per stage to make up the right length.