The linings were only a little proud of the ribs. I unrolled a long piece of medium-grit sandpaper on the workbench, and sanded the linings flush to the ribs. This only took a few minutes. A light touch-up sanding removed the random fibres, giving me a completely flat plane.
The glue from last time was still in good condition, so I saved quite a bit of time in not needing to soak and prepare a new batch of hide glue pellets. I applied a medium-thick coating to the linings and rib edges, and then a similar layer on the back plate periphery.
One can never apply enough clamps fast enough.... the glue was setting by the time I had the last clamps in place. I can only hope that it will still cure to a good strength.
I will be away on business for the next 10 days, so the clamped assembly will have two weeks to fully set. If necessary, I can apply hot low-viscosity glue to any opened areas and reclamp them. It shouldn't be necessary to separate the back plate and start over.