After the install Face Frame attachment - hard way to do it if you don't want to use trim screws or nails -
BUT - As you have set yourself up with splines AND if you have shelf holes bored I have done the following with good results:
Make up "pin board" - a 1 x 2" or 3" wide board as tall as will fit in the opening or thereabouts and bore matching shelf holes in it - at least every 6" or so. Using straight pin type shelf pins (or dowels) set your "pin board" into your cabinet side shelf holes. Glue up and tap your face frame verts in place and then hold them there with clamp pressure applied with clamps reaching to behind your "pin board(s)".
IT WOULD BE FAR EASIER if your face frames were preassembled. Leave only the very outside scribe verts loose for scribing and fitting. BUT as your top rail is one piece and you have access for pocket screws (or face screws if you are then applying some crown) the single stile at a time method can work OK. I might use "pin boards" on the mating side of 2 bookcases and use a caul across the two with clamps pulling from 2 pin boards at once. Would be a more direct pull. Of course you don't want the clamps to pull the verts tight - just to hold them there until the glue dries after you have tapped them into place with the splines. The idea is not to oversize the shelf pin holes.
With the right deep throat clamps you can sometimes hold 2 pin boards tight to the interior faces to help resist movement OR carefully screw 2 together using GRK type finish screws passing through the cabinet walls through the shelf pin holes. In this case you screw through a section of the "pin board" that has not been pre bored.
Clear as mud? Read twice and then if you are still befuddled I can try to be more lucid with my explanation. This method does work.
"... for when we become in heart completely poor, we at once are the treasurers & disbursers of enormous riches."
WQJudge