S-Pops,
1) Was this not posted 1/2 year ago?
Titanium welders are not too common.
But in SoCal they might be with the aerospace, and then also where there are bicycle frames.
Going to Boeing etc, will not result in any good outcome as they will sick the guard dogs on you near the lobby.
I would
not believe that "any performance shop" can it, even if they could, they do not likely have the materials.
So you will need the replacement tubing.
And welding rod if you can happen to find a TIG welder that is willing to try.
You will also need a back purge, so at the minimum some bungs, assuming that he has a multi-regulated system for "back purging" and "trail purging".
Since one would really only have the set up if they were doing titanium, you will need someone who specifically can do (read does) titanium.
Personally I would have him do a practice piece, on some extra tubing.
The set up for the regulators should be like the out of focus blue part in the picture... (The blue part with the three flow regulator)
So I would contact Santana Bicycles somewhere off the 10, or maybe the 57, as they will be able to steer you to who can weld it... If anyone can
I would suggest Titanium Joe (google) for the tubing.
I would use the flexy part. It is a good idea.
It is easier to replace that from over flexing that the muffler from overflexing... And they are made to flex, whereas a pipe/tube is usually not.
If the flexi is not lasting then there are probably issues with needing another one somewhere else down the pipe, or controlling the engine movement with mounts.
But the exhaust should be able to cope with the engine movement.
You should have the flexi close to the center of the engine's rotation on the mounts, which may be difficult with the manifold. It is easier on a Rover engine where the exhaust goes under the engine. On the Toyota the exhaust would need to come forward (aka blown diffuser style - which is clearly not viable), so I suspect that you need a flexi as close to the manifold as possible (not sure which side of the cat I would go though)... and maybe one closer to the muffler to take out bending moments.
There is a place in Laguna Nigel or Newport that does specialized motorsport bellows...
(wow I found it):
Reid Washbon Racing | Inconel Bellows - Stainless Steel Bellows
I would start with them, and I would probably contact Santana cycles as well to find a welder.
If you to Reid Washington, see if they have V-Bands for titanium. One on the Muffler side and then a regular steel or inconel one of the other side would make the job much easier, and very clean. I am interested to know if there is such a thing as a titanium V-Band??
Alternatively my offer of taking if you throw it away still stands from 6-12 months ago.