So, not even components, just soldered as LGAs..? Will that work? -- PCB is notoriously nonconductive thru-plane so it'll take forever to melt paste inside a sandwich of it. Castellated side connections are fine, or vias/thru holes of course, but those also sound awfully more conventional than what you must be after.
And how is that different from a multilayer board with buried vias? Why can't you route that on a single say 8-layer board, or optimize it down to 6 or 4 without stacking? A single board will be stronger, too, and not left with leaky (flux residue) gaps between pads.
You can throw whatever you like on mechanical layers, but it all has to be done manually, so you don't get any advantage from placing pads (pad stacks only generate graphics on the hard-wired layers).
Tim