I was previously very nervous about soaking the alloy base in acid. I took the boiler off tonight and there quite a few "calcium crumbs" that had loosened up and were free floating. I guess some of these had lodged under the flapper valve. When I tried to pump water through you could see it blow past the flapper valve.
This time I soaked in some double strength vinigar. It is still difficult to see what remains under the heating element, but it does look cleaner.
Pumped vinigar through the machine, and then flushed through with water. By the end there did not appear to be any water coming back through the flapper valve.
I have not yet sorted all the squeaking though.
I adjust the grind coarser, I am getting better results and the yield tonight was 28gr or 1:2 ratio, with a prime and 1 lever stroke.
Did not taste the shot though, as I have not been getting enough sleep with my previous tasting of an evening.
From the videos others appear to get more than 30gr from a prime and 1 lever stroke. What should I expect to get?

That's great news that you're making progress. There's a learning curve with this machine. I was going to say curvy beauty, but yours is not so curvy with the custom boiler.

The shot volume with the La Peppina is pretty generous for such a small filter basket. Seems you should be able to pull off around 40 ml from some past sources in some very interesting old threads, but honestly it's been a minute since I've got mine out so I don't have a good feel for it, but I like small shots anyway and usually dose 14 grams in this lever.

Lever machine with most single pull volume?

Incomplete list of Gravity-fed lever machines

Spring lever owners, do you pull a full volume shot?

By the way I did get some curvy beauty - when I got my bit from Sergio I could not resist getting a red replacement boiler. It does look much better even if it ultimately is not as durable as stainless steel.
I also agree about sticking closer to 1:2, rather than getting into the bitters. Only reel interest I have about the full shot yield is just to be sure I have full functuion.
I did use the thermocouple to determine the switching points, Off at 100C and back on at 95C.
Thank you all for your help.

No problem, Tim, I rather enjoy talking about the La Peppina. It was my first lever and I spent a lot of time learning to pull espresso and playing with temps and technique in the early days. I'll probably never part with it.

I am getting excellent tasting shots now.
But the machine still has an anoying squeak. The lever pivot has been lubricated, it is sounding like it is the top pivot up on the piston. I am going to need to make a jig to remove the piston from the base.
Listen to the video, there is a humming noise as the shot extacts. Not sure if it relates to the squeak. Or if it is from some leakage past the flapper valve which could explain the lose of yield? Anone ever heard anything similar?

The whistling Termomatica, I hear the sound, but I don't know what it is. It almost sounds like the ringing of a glass, some sort of high-pitched vibration.

Finally I can say the La Peppina Termomatica is fixed.
The lubrication hole for the lever bottom pivot had not bee drilled out in the factory, that was an easy fix.
The problem I had with fixing the flapper valve was that the retaining screw was frozen in. Before they invented electric shock drivers we used a manual shock driver that needs you to hit the end with a hammer while applying a twist on the body. The cast housing was put on solid block of wood and the kettle retaining screw bottomed out on the wood to directly absorb the shock load from the hammer blows, rather than the cast housing. Fortunately with only a couple of light taps the screw came loose.
There was enough scale build up on the housing valve seat to cause it to leak. I used a perfectly flat piece of 3/8" tool steel to scrape the scale off the valve seat. The flapper valve is still soft and pliable and appears to be sealing much better than before.

Wow excellent conclusion to this saga

The portafilter for the La Peppina is a very unique piece of kit. I could not find any other portafilter that could be modified to fit this machine. And I wanted to get a bottomless portafilter.
I have started on making one from scratch. The base is 51mm 304 stainless tube. I have then turned up three 8mm diameter lugs. I am still tuning the length of the lugs so that they hold the portafilter body central in the group. I also want the filter basket to just kiss the top of the group and lock up, unlike the factory portafilter that has stops. If this does not work then I can add stops.
The photos should help you understand where I am going.