The 2-20 is the same as the Edgware. Any of the available french-style mouthpieces will work. I use a Selmer HS* on mine and it works just fine. You might look at offerings from Vandoren ( B45, M39, M13) or the Rico (Now Addario) Reserve, or the Hite Premier. Any of these will work. Which one will work for you is a different matter.
There are often small differences in tenon size betwwen manufacturers, but for the most part, as long as they will fit together, then the fitting of cork of the appropriate thickness to the mouthpiece tenon will resolve the problem. If the Artley mouthpiece works for you, consider getting the mouthpiece cork replaced. If you have this done by a tech then take the barrel with you so that the tech can correctly fit the cork. If the Artley m/p isn't satisfactory then consider a replacement.