My Fostex backhorns pesented the same problem. I glued and nailed the innards into 3 sub-assemblies and positioned them on one of the side pieces.
Drew lines around them so I'd be sure where they went. Laid down a bead of polyurethane construction adhesive on the down facing-edges, PL400 (brand doesn't matter) and then placed the sub-assemblies back in position. Just used hand pressure to displace enough glue to see some squeeze-out and know the edges were reasonably flat against the side. Waited a bit for the glue to develop enough tack to hold the pieces against pressure (about 10 minutes) and then made a sandwich placing the second side on top and lightly clamped it on using cauls. Next day I removed the second side, put a bead of the glue on the exposed edges of the pieces and replaced the second side. I did use some finish nails to orient the side square against the top and bottom and then once more lightly clamped the whole thing.
The construction adhesive in a tube also eliminated the need for a sealant because it is a caulking. It's a permanently flexible adhesive/caulk that gives you a good airtight joint.
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