Luthier CNC

[Voicecoil]

If I were you I'd stick with 15mm (or even 12mm) on the gantry sides and add some reinforcement ribs (say 40mm tall) all the way up along the edges (40x15mm flat bar for instance) - if you do the sums it works out much stronger than thicker flat plate. Aluminium Warehouse are not bad for plate, even if not the cheapest and having had a slightly checkered history with some of us on here, at the moment they are giving good service, cutting plate VERY square and generally 1...2mm oversize: to select the cast stuff click on "grade" and select the bottom item from the drop down box.
If it were me I'd also be adding some plates top and bottom of your bed frame members to form like a "sandwich" structure and tie it all together in X and Y - though I can see that might have some weight problems for you.