This Moves This Way & That Won't? (the answer to the puzzle is - SPLINES)
The maple bench top core's width can change acrossed its width by between about 8 percent and 10 percent or 0.0027 inches/inch of width to 0.0035 inches/ inch of width. For the 20 1/2 inch core width, that's around 1/16th of an inch. The apron is either beech or birch so they'll change by between 10 and 12 percent or between 0.0034 and 0.00432 inches per inch of width - but each is only about 2 inches wide. Cumulatively they can move about 1/64th of an inch.
So how do you join the maple core to the beech (or birch) apron? Per Frank Klausz - SPLINES - 1/2" by 1 1/2" ply splines - in this case 9 ply baltic birch ply strips. An Onsrud two flute spriral end mill, the Micro-Fence connected to a Dewalt 621 plung router, the bench core resting on a 2x4 on the floor and clamped to the side of my assembly bench and it was router away.
The Micro-Fence on the router in the picture above, along with the Tite-Mark wheeled marking gauge, let me transfer the top of the spline's groove to the inside of the bench apron. Set the fence from the top of the apron down to the top of the core's spline groove. I wanted the apron to be about 1/16th inch above the top of the bench core. Dial sixty three thousands (0.063) on the fine adjustment dial on the Micro Fence and route away on the apron parts. This precision probably isn't necessary for this application but if the fence system will do it I use it. When I do line inlays or band inlays the precision fence really shines.
The splines are ready to go. Need to glue them to the apron( they'll float in the grooves in the bench core) , and while I've got the apron apart I'll screw in the Veritas Twin Screw "nuts" into the inside of the apron and may or may not glue the apron together. The joinery, along with the all threads connecting the front to the back through the core may not require glueing the apron together. The shoulder vise arm probably won't need glue either.
Because 1/2 inch ply 1 1/2" wide splines align the apron to the maple core, the joinery of the apron and the order of putting its parts together is important. It's the mortise and tenon joinery on the shoulder vise end of the front of the apron that complicates things. Study the Apron Assembly Order diagram below and the order of assembly will become "obvious".
IF I'd used thicker stock for the Twin Screw Vise end of the apron I could've mortised the blue screw guide nut into the back of it rather than surface mounting it as I had to.