That set-up looks very stable and certainly frees up your hands to do a careful job of aligning rod with bore, thereby protecting the muzzle.
I use a Tipton gun vise. Not the real expensive one called the "Deluxe" but just the standard one. I think I paid about $40 for it several years ago from Midway, but I now see them at Jerry's Spots (wholesale) for around $35. The deluxe one is going for closer to $80.