Spoiler Alert!  I fabricated one of these and it didn't work.  Actually went a bit slower.  Ya win some ya lose some.  If any of you have better luck please share your experience.  DBM 6/6/21.

On my recent post regarding cylinder head flow, I mentioned that I had come up with a design for a special insert that bridges the gap between the cylinder head 1.3” diameter exhaust port outlet and the header pipe 1.27” diameter inlet.  When used on a head with a stock port outlet, in conjunction with the stock header, the mock insert showed a 4.2% increase in average flow and a 5.3% increase in maximum flow (139.5 CFM vs 132.5 CFM).  This 1.3” insert doesn’t work on a head that has a port outlet larger than 1.3”.

I tested the stock header on a head with a 1.5” diameter outlet and a special insert like the one described in this post, except the insert OD & ID were enlarged so that the ID of the insert matched the port outlet (1.5”).  The other dimensions on the insert remained the same.  When used on the modified head with a stock header pipe, the special 1.5” ID insert showed a 2.0% increase in average flow and a 2.8% increase in maximum flow (152.9 CFM vs 148.7 CFM).  Every little bit counts.  While I don’t suggest that you run a stock header on a port outlet larger than 1.3”, if that’s all you’ve got, the special 1.5” ID insert will help a little.

I used 28” H2O test pressure for my flow tests.  I wanted the air moving as fast as possible.
 
The concept behind the special fitting is to provide a uniform cross section flow path from the port 1.3” outlet to the pipe 1.27” inlet.  It bridges the void resulting from the diverging bevel on the outlet, the .20” thick gasket, and the converging funnel in the inner pipe leading to the 1.27” pipe inlet.  The following sketch should give you a good idea of the problem area.

You can see there is no longer a void at the port outlet.  It’s a straight shot out of the port and through the insert.

This is a detailed sketch of the special insert.

Note that there is a filler/sealer between the insert and the port beveled face.  IMO, you can use a high-temperature RTV or some of the JB Weld Extreme Heat paste I’ve been experimenting with.
 
To install the fitting:

Position the engine at TDC on the compression stroke.  The exhaust valves must be closed to prevent entry of debris into the cylinder.

Take appropriate measures to keep grit and chemicals out of the port.  Fill the port with paper towels or some other suitable cleanliness barrier.  Don’t get any grit in or around the valves or guides.

Clean up the beveled face on the port with sand paper.  Do it by hand so as not to spread grit and debris into the port.  

When you finish sanding, vacuum the port out to get ALL the grit out.  Wipe down the cleaned beveled surface with a towel and appropriate solvent to remove any residue, oil, etc.

Remove your cleanliness barriers.  You will most certainly regret leaving a paper towel in your exhaust port.

Apply a layer of your favorite (very high heat) sealant to the beveled face.  Put in the special insert as shown in my sketch.  Use the header pipe clamp ring along with an appropriate spacer to clamp the insert in place. Carefully wipe out any sealant that squeezes out into the flow path.  The flow path must be free of sealant.

Let the sealant cure for a day.  Then remove the clamp ring and spacer.  Install the gasket and then the header.  If you really want to do it up right, get some stainless-steel bolts exactly 4mm longer than the stock clamp ring bolts (make sure to use the correct diameter and pitch bolts).  That way you will restore thread engagement to original.  The insert has a .16” thick flange on it so you will lose 4mm of engagement.  The 4mm longer bolts will restore the engagement.

Go test it out.  I can’t guarantee that you’re gonna feel a rush of horsepower, but hey, a 5% increase in flow ain’t gonna hurt.

That's a good suggestion on the thinner material for the flange and passing through the tube.  Still have to maintain the .945" dimension from flange face to end of tube.  You probably will have to hand fit the inlet side of the tube to the "torque cone" to make sure that the insert flange makes-up properly to the face of the cylinder head socket.  I would still use a filler or sealant to prevent exhaust gas from running between the insert and the face of the head socket.  On my mockup, I incorporated a feature like you describe.

I was really surprised by how much this simple insert improved flow.  I wish I had tried something like this on my bike when I was running the stock head pipe.  I have the Mac header sort of permanently attached to the muffler.  I don't want to disturb the joint.

Here's what my simulation of the pass thru looked like.

I looked at these Durabond products when I was doing my filler tests.  They have a minimum $100 order requirement, and I would have to pay the shipping to Hawaii.  The stuff looks promising, and they have one with an aluminum filler which would help keep the coefficient of expansion closer to the substrate coefficient.  But for me, it would be cost prohibitive.  I could lay out about $150, and then test, only to find that its not suitable for what I want to do.

Have you tried the aluminum brazing rods yet?

Back in April I did this I made the insert project through the disc until it touched the cylinder head welded it in place at that distance and then
bedded the contraption down onto manifold sealant and followed it up with the gasket and flange   I replaced the header setbolts with threaded stainless rod and used dome nuts over spring washers to refit it.
The flow must be better by making a smoother path but to be honest I have not noticed any difference in performance in the six months or so since.
The tube and disc were made from 1.6mm stainless.

Unfortunately no photos

I made the tube from a piece of stainless tube that was a little larger than the required diameter so I split it and rewelded it to suit.
The new flange was made of similar thickness stainless 1.6mm

My 2012 bike has 150 main jet 52.5 pilot and 3/4 spacer 2 turns open on screw
Dyna muffler with catalyst  stock head and header mostly run at sea level

I am happy with the way it runs
Just because I didnt notice much improvement at that time  does not mean that it hasnt improved I have no way of measuring the difference if any.
I would say it certainly has not got worse and seems to be improving and running smoother the more miles I put on it
I have 9000kms now
At about the same time 7000kms as I did the insert mod I changed to Penrite mc4st full synthetic and noticed the gear changes less clunky
so maybe that has made the engine smoother as well?
Sorry to be so vague and seat of the pants