Here is a pic of the tapered punch positioned on a 5/8" diameter 60 mesh SS screen. You can't see the other part of the forming die but it is a tapered hole that matches the tapered punch.
After pressing the screen into the form it looks like this
This a side view of a finished screen
Notice the sides are tapered a bit. The best measurement for the 14/20 joint taper I could measure was about 3.8 degrees. The tapered side is about 1/16" high so that gives a good bit of surface area holding onto the inside of the stem. For the screen to be pushed through the stem the top diameter has to get compressed. I inserted a screen into a female stem and stood the stem upright on a scale. Then I pushed down on the screen with a small dowel rod. The scale registered 2.5 kilograms before the screen came loose.
These can be retro fit to an existing unit. More in a bit
Here is a wood positioning dowel, I had to make the end a little smaller in diameter
Then you slide it into position
It is pretty easy to tell when it is seated.
You can see where the male stem ends, just a tiny bit above the screen.
I need to figure out how to put a "stop" on the positioning dowel so you can't force the screen through.
I'll be sending some of these off to testers and confirm that it works and I'm not missing something just because I like this set up. The other solution involved custom glass stems which I almost had made, thank goodness I ran out of money. That would have been several $K down the tubes.
Thanks again to
@Fat Freddy his question made me think.