There's a lot of confusion around lead-carbon. The biggest reason is that carbon is used in different ways, with different results. I'm no expert, but as I understand it has uses of at least:
1) as an additive in various forms to the electrolyte.
2) as a kind of shield over the cathode plate, providing a physical matrix.
3) as a separate, secondary cathode. This configuration seems the most interesting. It results in the battery taking on significant super-capacitor characteristics, with some tremendous and well independently tested advantages.
This third type was developed at CSIRO, the Australian Governments science research agency.
It was then spun off as a business entity, branded as 'UltraBattery' (/eyeroll) and they went about finding national licensees to manufacture the technology.
And tried to convince the world that PbC ultra batteries were the obvious replacement for NiCd batteries in electric cars. (/facepalm)
And around then of course Lithium 'happened'. And later the business was sold cheap, then the purchaser effectively shut it down completely a couple of years after that.
It appears that the situation now is that there are a few licencees still ticking over, who obviously want to protect their patch, but with no licensor enforcing the IP rights globally, the legal situation is murky.
Step up a few competent Chinese manufacturers who have realised that there is an opportunity here
And many many many Chinese battery manufacturers who use the words 'lead carbon' in their product descriptions and titles for regular AGM/VRLA because SEO.
Anyhow, that's enough for one post. My advice when searching for lead-carbon is to look for references to 'ultra-battery' or ultra- or super-capacitor in searches and on sites.
After a ton of research, I recently purchased 8x 200Ah 12v PbC at about US$350 per battery FOB Qingdao.
Datasheet:
https://drive.google.com/file/d/1MerAE4sKDNURqRWWMckT9Vfi57UReP_m/view?usp=drivesdk