Again, rather tediously, I agree with Jim.
The only way for your canaries to to do anything like weighing seriously less than eight tonnes, is to remain virtuously (or obsessively) in the cage, perhaps not noticing that there is no bottom at all.
However even then there are complications. The birds are keeping themselves off the chassis by propelling a stream of air downward, right? That means that they are removing air from inside the vehicle. So air must come in to replace the lost air. If the air comes in from the top then it drags down the cage. If the top is sealed, then it must get sucked up from below, sucking down the cage.
Right then... have trained canaries in a cage of with walls, but neither roof nor floor. Yes, but although this would greatly improve the load on the chassis, it still would produce a down-force on the cage unless the walls were perfectly streamlined (which is absurd, as they say in Euclid!)
Well, then go the whole trained canary, and omit the walls as well. OK, now we are getting somewhere! Not only is there no cage to intercept downdraft, but when the downdraft hits the ground, it gets deflected beneath and behind the vehicle, propelling it foward and applying lifting forces into the bargain. Get the parameters right, and you could enjoy the sight of eight tonnes of canary fluttering behind your truck, driving it according to the truck driver's requests.
I hope that was articulate. I have been typing over a pile of importunate cat. A more serious obstacle than it might sound. Perhpas he was attracted by the canary topic...