Hi Dave--
First, welcome to the forum. From your post it sounds that you are capable of doing some light machining and metal work. I have converted a battered No 4. MK2 to a single shot .22 Long Rifle. Like Peter said I would keep it simple. If you can find a Numrich .22 LR conversion kit I used the .22 LR barrel liner from the kit. The kit was originally for the No 1, MKIII Lee Enfield but the barrel liner will work in the No 4 series Lee Enfield Rifles. I also used a C No 4 MKI .22 complete bolt head assembly. You will also have to cut the firing pin tip off for the rear firing pin to properly engage the new .22 firing pin in the C No 4. MKI .22 bolt head assembly. You can either strip out the magazine follower and spring or leave it in. I found a C No 4 MKI .22 follower which has hole for the spent cases to fall through.
After you obtain all of the parts, assembly and headspacing is quite easy. Thoroughly clean and degrease the barrel and chamber, and the .22 LR barrel liner. Plug the end of .22 LR barrel liner to prevent cement from getting into the .22 liner bore. Also coat any part of your rifle with a epoxy releasing agent that you don't glued. Using a slow setting epoxy based cement (Can be found at Brownells) lightly coat the .22 LR liner. At first slowly push the .22 LR liner into the .303 barrel approximately lining where the extractor groove would be located until you can place the complete .22 bolt into the gun with the bolt head engaged into it groove in the receiver. You did not indicate if you had a No4 MKI or No 4 MKI* Rifle. When you place the complete bolt the rifle make sure the bolt extractor is lined up with the extractor groove on the .22LR liner. Make doubly sure that the bolt and bolt head assembly has epoxy releasing agent on them. There is nothing like gluing the bolt into the gun. Very slowly push the .22 LR liner into the chamber and barrel with the bolt until the bolt fully seats locks into the receiver. This action will set your headspacing. Excess expoxy will come out as you pushing the .22 LR and bolt into the .303 barrel. Do not pull back on the .22 LR barrel liner at anytime during this process. May sure no epoxy gets in between the bolt head and the .22 LR barrel liner as this will throw off your headspacing. Do not remove any excess epoxy at this point. After several hours when the epoxy has semi-harden you can remove the bolt and clean out the excess epoxy in the chamber area. I would wait until the epoxy has completely hardened before you do anything at the muzzle end as you can possibly move the barrel liner at the muzzle. When the epoxy has hardened you cut the excess barrel liner at the muzzle and properly crown the barrel.
If you can't find a Numrich Lee Enfield 22LR barrel liner. You will have get one made up from a .22 LR barrel liner and .303 Britishcartridge adapter and chamber the .22 liner for .22 LR. But assembly will be basically the same. I hope you found this helpful. Sorry for being a little long winded. If you have any questions please let me know.
--fjruple