I probably sound like a broken record (again!) but the critical aspect is really weight distribution. Sure, 11 lbs minimum weight is sensible, but it HAS to be concentrated between the hands.
A big heavy barrel to get the overall weight above 11 lbs is seriously counter-productive as the rifle will lose "liveliness" and will feel like a muzzle-heavy truck axle to shoot, and a log to carry.
Also, when a heavy barrel rises with recoil it gains momentum and the leverage from excess muzzle-mass will drive the comb into the shooter's face, significantly increasing felt recoil.
A heavy full-diameter breech-section of the barrel is crucial, followed by significant taper to the muzzle.
Look at the barrel profile of the current .500 Jeffery bolt-rifle, or better still the stepped-barrel profile of vintage Jeffery big-bore rifles (visible in the images of 458Win's and Claydog's rifles on this old thread).

...and as you indicate, Rolf, adding a heavy steel buttplate at the extremity of the stock to "balance" a muzzle-heavy barrel, is certainly not the answer!

With a single-shot, it is difficult to add weight to the centre third of the rifle, as you are limited by the action itself, and you don't have an extra pound of bungers in the box to "soften" the first shot. But choosing dense walnut, as Mike suggests, is a good start. Not sure about Euro suppliers, but Roger Vardy in Australia (who advertises on these forums) offers three densities in his stockwood to choose from: Light, Medium & Heavy. All stockwood suppliers should do this!