Yes, probably. It depends on the thickness of the metal at the end of the shank. The very end can get pretty thin and still work, but of course you would not want to drop it because it is more easily dented. If you have a good shop near you, this would be the simplest and cheapest option.
Maybe. Just for fun, find a trumpet (not cornet) mouthpiece and try it in there. I suspect it will fit very well. This looks like my old tenor horn, which was in baritone-range Bb but had a trumpet-size receiver. So if it is a standard trumpet size, Doug would have to have a trumpet-size shank and he mostly deals in low brass. So you should contact him and ask that question. If he has the right blank, then see if he can put a cup on it like a 6BS.