Unless you can have the lug removed and welded back on after having the barrel cut off at the chamber end, it's not going to happen.
Another option would be to 'stub' the barrel, cut off the barrel in front of the chamber area, bore it out and thread it, so as to screw a piece of suitable barrel material in place, possibly the remains of the original barrel, and then ream the .218 Bee chamber. Some care will be required, to leave enough barrel around the chamber to be safe.
Find a .22 Hornet barrel (which may still be a bit too long a chamber), or find an aftermarket source for a suitable barrel. Or a lug to weld on to a section of barrel. Sadly, most of the suppliers that specialize in such, are State-side, adding a great deal to the cost to import, or at the very least, adding a great deal of time, if you do up your own paperwork and find a seller that will ship across the line.
Also, for your own reference, find a chamber reamer dimensions print of each cartridge. You will find that the .223 is far longer than the .218 Bee. You pretty much need to be able to ream out the entirety of the former chamber to make a decent job of it.
Anything is "possible" if you have enough money or time to throw at a project. The possible sometimes collides head-on with the practical, though.
You can always load down to matching velocities if it's about the performance. .218 Bee is a cool old chambering, but being based on the thin walled 32-20 case as a basis, I don't think I'd go too far out of my way to take a barrel that was working well and try to convert to it.