Hi Jim
No, I didn’t miss it. I have already tried doing what you suggest, and I have to report that it ain’t easy! It is easier to form the alloy used in the tube than the 6Al-4V alloy, but only slightly. Very large forces are still needed.
I would have to develop new steel dies for this, and hope that a 10 ton press is sufficient for the forming job. I have some reservations, but maybe. Many months of work would probably be required.
I would have to ‘seal’ the joint line to prevent local oxidation and corrosion. While the surface of the Ti tubing does develop a very effective protective oxide layer very quickly on open surfaces (humidy helps, believe it or not), Tim Clarke’s experience is that tiny pin-holes through the metal do ‘burn’ out rather quickly. I suspect that the butt joint on the surface would behave in a similar manner to tiny holes. So, how to seal that joint (or several joints)?
I don’t think there are any ‘sealants’ which would handle the high temperatures AND the thermal cycling.
I don’t think ordinary spot welding would work here.
You can’t braze this stuff.
MIG welding might work – after a lot of practice at sheet metal welding, but I don’t have a MIG welder and I have no experience there either.
An electron beam welder would probably work, but I don’t have one (and cannot afford one either).
But more to the point, what would the design gain?

I have superimposed the parabolic design (red) onto the parallel tube design (black) here. The volume difference in the corners is small – remember that the OD of the tube is only 38 mm. The flames are kept out of the corners to a large extent by the flow of air in through the inlets as shown. The main part of the flame vortex is up near the splash plate anyhow, although burning up the middle certainly happens.
So – given all this, would the behaviour of a conical/parabolic burner chamber be all that much different from one made from straight tubing? I have to say I cannot see that there would be any real gain for all the hassle.
But I might be wrong. Perhaps someone might like to make some parabolic chambers for testing? I would be very willing to give them a test!
Cheers