Some observations based on my experience converting a .303 to .22...
This wasn't a rifle I converted, it was a pile of parts made up into a rifle. Good use for a barrel with a ratty bore.
When you close the bolt on a .303 rifle, you will notice that the boltface does not reach the barrel breech. This is because of the .303 rim.
No. 7 barrels extend back into the receiver to reach the boltface.
A longer .22 bolthead would accomplish the same thing, but this would complicate other parts of the conversion.
I machined a chamber insert that looked like a .303 cartridge case, including rim. Installed this in the barrel. Ran the piloted liner drill through, so the bore was the right size, end to end, including the new chamber insert.
A .303 firing pin can be converted into a striker rod to hit the firing pin in a rimfire conversion.
If a No. 7 bolthead and firing pin cannot be found, a .303 head can be altered. Anneal the bolthead. Solder a plug in the firing pin hole. Carefully lay out and drill a two diameter hole for the rimfire pin. Make a pin to suit.
If a No. 7 extractor cannot be located, it will be necessary to make an extractor.
Once the barrel is installed, and the .22 bolt is fitted, bond in the liner, and ream the chamber, getting correct headspace. Make the extractor cut.
It is an interesting project. The resulting rifle is not unlike a British No. 9 rifle.
If I were to do another one, it would be based on a SMLE.
It is my understanding that Brownells will export the Redman liners, with the proper paper. The standard is too short, although there is no reason that the muzzle of the liner could not be set back in the muzzle of the .303 barrel. The longer liner is a lot more expensive.