Have you tried knocking up an internal frame out of Unistrut and epoxying the wood to that ? That ought to hold it round the edges and if you’re worried that it might bulge or dish in the middle you could fasten a stiffening cross-member made out of an offcut onto the back.
Bit of a quick n dirty one to get me going with the new toy. Used an existing Mahogany frame, a top plate made from an old spare layered ply shelf finished in Oak, infilled the lot with some Oak off cuts and the base was made from a couple of pieces of Birch ply. Popped a bit of damping between the base and the Oak infill. . Soundboard is an old aluminum one I had knocking around, fitted some Track Audio feet and bingo, away we go.
Will now have to engineer the full on plinth for a 401, for now this is rather good. Top job on the 401 Matt.