Sure here you go.
This is the major one "Egge Machine Company" in Santa Fe Springs, California, this is a great Company that my Dad and I started using way back in the 1960's when we were restoring the Model A Ford's. They will have listings for most or the engine parts needed to do a complete rebuild on both the H & G series Flathead six's. Here is one link for the G series Parts the all these parts and several others like the Connecting Rod Pin Bushings are also available separately and they do have new Pistons for them too.
https://egge.com/product/ford-226-l6-1948/
Here is one link for the H Series 226, all these parts and several others like the Connecting Rod Pin Bushings are also available separately too. They don't seem to have any new Pistons listed for the H series though six's though.
https://egge.com/product/ford-226-l6-1941-47/
But they also have a rebuilding service for Oil Pumps, Water Pumps, Fuel Pumps, plus a Camshaft, Lifter, & Crankshaft Regrinding Services too that you can ask about. I will put one link for the 1941 to 1947 226 H Series Flatheads also that shows most of the parts they have available for them.
Red's Vintage Parts Red's has a few NOS Ford G and H series Flathead Six Parts available and even some Cylinder Sleeves, as well as full overhaul Gasket Sets. this link is for the H series engines
https://reds-vintage-parts.com/store/category/24-ford-h-series
Best Gaskets has new Full and individual Gaskets for the G, H, and M, series Ford Flathead Six's this link is for the H series.
https://bestgasket.com/vintage-engine-gaskets/
Here is one listing for a new set of Pistons.
https://www.ecklers.com/ford-pickup...6-6-cylinder-choose-your-size-48-18087-1.html
This company Arthur Gould Rebuilders has a Fuel Pump and Water Pump Rebuilding Service and also some exchange Pumps.
http://arthurgouldrebuilders.parkerspackards.com/mobi/
Van Pelt Sales has some Pistons and other engine rebuild parts in their parts listings, and they also have replacement parts for the Chassis and a rebuilding Service for these old Transmissions, here is the link.
http://www.vanpeltsales.com/FH_web/vanpeltcatalog2023.pdf
Schneider Racing Cams has a Camshaft (and think also for the Lifters) a regrinding service for stock or a more Performance grind.
http://schneidercams.com/regrinds.aspx
There are several other Aftermarket companies for Custom made Forged Pistons if you are going to a more Hi Performance build let me know if you need that kind of info. Hope that is of help to you, best of luck on your rebuild. I am also working to set up my shop to restart my business of repairs and rebuilding of engines and other parts of these Classic Cars and Trucks. Edited with some additional info.