Another option that works well would be to take it to a machine shop and get it into the hands of a turner.

The current barrel can be cut off in front of the barrel reinforce and the stub bored out to accept the threaded end of a prepared barrel. Any Lee Enfield barrel could be used, or a blank with your choice of caliber.

When done, and if done well, the original serial number and markings will be preserved and the only mark to witness the modification would be a fine ring line in front of the reinforce where the two meet.

Just noticed that your rifle has a rib which complicates things. 'Engine turned', it isn't a separate piece, but is a solid part of the barrel, is it not?
So belay my last, this maybe not the easiest route.