Here we go again!!!
Alas, it is not just the mass of a metal object that determines it's "stiffness".
With metal, form is part of function. You can remove metal, and make it weaker, but also you can remove metal and make it stiffer. It depends upon how it is done. Or rather, the form of which you do it.
Example:
Take a piece of sheet metal, like you would fashion ductwork from. Lift it up from one end, it's flimsy, easy to bend.
You can take it, and put it in a break, and bend it just enough to make a raised "X" across it. It is much more stiff now.
Now take same kind of sheeting, and drill holes in it. Along the holes you raise the bend the lips up. It is much lighter, and much stiffer now.
It is not just a form of mass. what kind of metal, the heat treating, and the form all have effects on metal.
As for the OP's original question, you may want to contact Douglas, or Hart, They make barrels, along with fluting, so may for a price be able to do yours.