Not really sure what the filler piece not being square/parallel/whatever has to do with any of it.
You say you've got one straight edge. That edge will go against the straight edge of the bookcase. The other edge, no matter how ragged it is, goes against the ceiling and all that raggedness gets cut away and a new "raggedness" (that precisely matches the ceiling profile) gets added.
I'm not really sure what the point of that u-scribe jig is* (I just took a brief look at their site). All you really need to do to scribe is to ensure that your straight edges are parallel, that the narrowest point of your scribe board is sufficient to fill the gap to the ceiling, then use a compass like this one from u-scribe (or any cheap Dollar/Pound Store version) to run along the ceiling and make a line on the filler piece.
Cut along the filler piece with a bit of a back bevel (makes it much easier to fit the scribed piece in), then install.
*I've gone back and looked at that product several times now and still have no clue what it's for or how to use it. I guess UK installers just come with the knowledge of how to use that gizmo built in, and it's likely well above the heads of us US-based folk... :shrug: