I have also thought of a MN bull barrel, like the Finn TKIV 85. When I see how well some of my MN shoot, I can only imagine with a precision heavy barrel.
I will tell you, the outfits I found charge ~$300 for a heavy barrel, and not installed.... and perhaps not chambered. A chamber reamer from Brownells is $100, about as much as a good gunsmith would charge to install.
Which brings me to my next "experiment" I have got several excellent barrels from Buymilsurp.com. He has a pile of MN take offs, some excellent+, check it out. I have a thrashed sewerpipe barrel and plan to remove it and put on a newer quality surplus barrel. I have done M-1 Carbine barrels, but they index super easy. Lets see with Mr. MN.
I will say if you go down the heavy barrel road, there is a Richard's Microfit stock company, gorgeous laminated or regular sweet black walnut, 97% inletted for a MN. They will put the channel you want on several types of serious target stocks. Obviously, free floating with a bedded receiver. So I work on the dream to.
I hope this has been of some use. Ciao