BSA Lee-Enfield .22 Conversion

I bought my second Lee-Enfield rifle last weekend at a gun show.  It appears to be a BSA SMLE converted to .22 rimfire as a trainer, and which has been subjected to "improvements" by later owners,  such as installing a Redfield rear aperture sight, modifying the frond end cap and front sight, removing the upper wood, and installing a butt stock with a pistol grip. It came with a spare, original-style butt stock and butt plate. I am not planning a restoration, but if it shoots well, I will probably try to replace the missing wood and metal parts. 

I can't seem to find a date on it. The wrist just says "B.S.A.Co." on one side, and "Short 22 II" on the other. It has what appears to be a 4-digit serial number stamped into the barrel and the action. The barrel does have" '39" stamped on it, but I understood that the presence of the volley dial sight means that it's a 1916 or earlier rifle.  The front barrel band has "EFD" stamped into it. 

I'd welcome any insights on the model and date of manufacture or conversion.

Especially with a rear dioptre sight.

Is the forend cap different on the .22 rifles than the others? It seems that the end cap on my new rifle is not like the earlier versions or the Mark 4 - it's shorter, and one piece. 

It also looks like it may once have had a bayonet lug, which was cut off. 

There are some similarities to a one-off Lee-Metford conversion I saw a photo of (last photo), such as the lack of both wooden hand-guards and the way the barrel extends past the end cap. 

There are also some similarities in the forend cap to this Sht 22 II I found on a "for sale" post. I see that it's a 1912 conversion. Mine also has a full .22 barrel, not a sleeve. Perhaps mine is an early conversion?

Also, both of these appear to have, not a bayonet lug, but a sling swivel, on the end cap. That seems likely to have been what was cut off of mine.  

Thanks! The forend cap on that 1901 .22 rifle looks the same as the one on mine - or at least, what it would have looked like before somebody cut off the sling swivel.  Hard to be sure from the photos, but the clearance between the barrel bands and the barrel one mine look like there could be room for forward handguards.