I thought that might have been how you did the billet - sure does look good.
I did my first copper billet in the forge and had a problem with the copper melting. The last few billets with copper I've done in the HT oven so the copper can be kept just below the melting point. With the oven I've both welded the edges to seal the copper, and also with no welding, just wrap in SS foil, heat and set the weld in the press. Well, it's not actually "welded", but more like "pressure soldered".
I "think" I like your method of having the copper about 1/8" inside, then seal welding the billet.
Again, a job well done on that Bowie.