You've got me all confused Morris. You say they are too tight for a wad. Did you mean too tight to patch?
I don't think I would shoot them bare balled. Green Mountain barrels have fairly deep and sharp rifling. There's a good chance they would lead up the barrel and it would be a bear to get that lead out. Jo-Ann Fabrics has some "pocket drill" that's pretty thin and makes good patches. I found some that mic'ed .008. That may work with your buckshot, even if you need to use a mallet on the short starter.
If you can't get them loaded with even a very thin patch I suggest you give up on using them and buy some .310 Hornady balls.