JMG.... Tommy Kelly and Donaldjr are correct about the glacial slowness of Hoppe's in desolving copper, and the aggressiveness of strong ammonia dopes, like "Sweet's 7.62." Another rapid copper juice is "Eliminator."
I do not leave those super dopes in the bore more than five minutes. Sweet's weakens with age. Eliminator, not sure. Eliminator is said to be safe to leave in bore, but I specifically would not. In my own little "test," I found Eliminator----which I consider one of the best copper dopes----offers zero protection against rust; may even promote it.
Hoppe's is the ONLY solvent I trust to protect a bore. Hoppe's may be left in indefinitely in a dry temperate or cold climate. Nothing short of real rust inhibitor or coating protects against rust in warm humidity.
Back to copper fowling... Ruger released the Super Blackhawk with 10-1/2" barrel in 1979, specifically to conform to the IHMSA Production Gun rule. (Production barrel length limit to include the XP-100 .221 Remington Fireball, with barrel just over 10-1/2-inches. Note: that is the only bolt action allowed in Production.) Ruger sent me two, one of which I scoped with a Leupold 4x, the other one I put to work in silhouette.
The iron sight SBH, which I soon dubbed the "Silhouette Super," had the standard Ruger .44 barrel made by George Wilson (Connecticut), with broached 1:20" rifling. Thsese barrels could vary, but this one was tight----.428" groove diameter. And a bit rough. It copper fouled badly.
I cleaned the bore with J-B Bore Paste rubbed on cotton flannel (my all-time favorite patch material), pushed & pulled on a 3/8-inch birch dowel. I carved a jag on the dowel with a pen knife. Careful stroking, with renewed applications of "J-B Paste" smoothed the rifling until very little in thew way of copper streaking took place. That gun went on to win the International Revolver Championship, and Hornady, Ruger, Smith & Wesson, and Federal championship trophies, among many.
This was the revolver that made the single shots realize in no uncertain terms,THE REVOLVER CAN DO IT.
As your Alaskan is a .44, the 3/8-inch dowel with carved jag, in conjunction with J-B Paste on cotton flannel patch, should reduce fowling to a trace, and make your barrel happier with cast and jacketed bullets.
For a .45, a 1/2-inch dowel, sanded down, might work better to keep the patch firm. J-B Paste is soft and breaks down quickly. It has none of the destructive aggressiveness of lapping compounds. Please let us know how it turns out, should you try it.
As a final note, I am careful to not pull the patch out the muzzle except to replenish J-B or replace patch.
David Bradshaw