I realize you already bought one, but I bought a Mech Force (link below) and it is very similar to the Bald Eagle.
I've used it twice now and it works really well. It has leather to go between the jaws to eliminate any marring of the barrel. I also bought some resin to put on the leather so the barrel doesn't slip.
From doing so research and just seeing what everyone else is recommending, and asking some of my bud s they all highly recommend this vice and I found out he is close. Great guy simple design and can add leather if need be as added protection
Sorry to further jack this thread up, but even though its a bit more expensive than other barrel vices, the new SAC is something to definitely look at:
I bought a Mechforce to remove a Tikka factory barrel. With the leather pads it couldn't grip a damn thing. Replaced them with 3 sheets of plain printer paper and it held the barrel solid as a rock and didn't leave a single mark it. I emailed the company and said WTF are these leather pads for, then?
I think @padom is right, I'm happy that I can make my Mechforce work but I don't know that I'd buy it again.