A couple thoughts:
First, the go to material for the GD cabs is 13 ply, marine grade Baltic birch. This is a high grade void free, resonant free Baltic Birch ply and is usually imported. You may be able to find sheets locally, or online.
Second would be the precise joinery used to construct cab. Dados, or mortise and tenon were the preferred method and guaranteed a very rodust, rigid cab
Acoustics: a speaker will coil (+ wave cycle) and recoil (-wave cycle)
Parallel walls within a cabinet will cause reflection from speaker coil and recoil. Reflections can lead to "flutter" phasing issues and other very unpleasant residual sounds. When the speaker baffle, 4 inner walls and back are assymetrical then you deflect any kind of reflections away from each other rather than towards each other. This allows the acoustics of sound to dissipate and decay with very little interference between sound waves.
However, there is a serious science to cab design, acoustics and sound reinforcement. That's why high quality sound gear gets so pricy. This shouldn't be discouraging, but more of an insight into intricacies of sound. I have built a couple amp cabs, both with dovetail joinery, quality woods, hand built hand wired 5e8a tube circuit and quality speaker. Both cabs are air tight, closed back cabinets for maximum punch and limited bleed through from sides and rear. Stick with very hard wood, tight joinery and Quality speaker. Preferably a closed/open back design where you can experiment by removing back panel, using absorbative foam treatment when closed etc. You'll probably be pleasantly surprised by the results