Then use stainless or maybe a bracket to steady them.
Could use stainless, but why over mild steel? Chrome moly is probably a better choice than stainless, and nearly as light as aluminum. Could use aluminum, but you'd want at least 0.25" wall thickness, then welding it would take significant heat.
CroMo would be my choice for strength and weight and is very common today in lots of exotic bikes as the tubing metal. 0.083 thickness mandrel bent should easily do the trick.
Some of the Rickman 750s had no backbone, which seems to maybe offer you the space you were describing. I think the biggest challenge you'll face is incorporating the Honda motor into a suspended stressed member based upon where the factory mounts are.
I've seen folks fab brackets for the rear of the motor that tie into a backbone (eliminating the rear hoop and suspending the rear of the motor) and do the same in the front, but they always tie into a backbone and the "bracket" is quite substantial in billet. I am very interested to see how you solve it!
I agree with Cal about chrome-moly tubing. It'll give you better strength and lightness compared to mild steel.
Since you are using a modern motor you will not have the same mount constraints as with the 750 motor. Of course, as you know, you then need open space in place of the backbone to mount your carbs.
The engineering required definitely has my attention. Does your CAD program allow you to place the engine and carbs in empty space, then overlay the top shape of the tank, and then weave a frame around it using the mount points? Given the constraints, I think you will need to cut the bottom of the tank and create a new bottom to fit your frame and carbs.
