I suspect that rigidly bolted side panels (not just edge mounted with the stock clips) would go a long way toward making it stable.
(Much like how the wood sheathing on a house frame adds significant shear strength to the walls.)
A cross brace or two on the front side would be an inconvenience for part removal, but might be worth it to help keep the frame front extrusions from bowing.
Come to think of it, I wonder if with 800mm extrusions, you might have issues with them being not straight enough along that length from the factory?
Another complication would be if this was to be enclosed. At that height, maintaining a consistent chamber temperature would require some extra effort.