Heavy Metal is a combination of Hevi-Shot and steel, for reduced costs, and they do not tell you the density of the Hevi-Shot included even. All Hevi-Shot used to be like a 12 specific gravity, which is great, but now they have become a brand name with several different densities, and they are very coy about what is what. Last time I really dug into it, Hevi-Shot Goose was still the old stuff, and it got lighter from there. Duck is lighter for example. Dead Coyote is still the old heavy formula, too. A friend uses/used some Federal Tungsten Iron BBs and said they worked well, but unfortunately right now about all you can find in tungsten from anybody is Hevi-Shot and Kent Impact tungsten polymer. The Kent stuff is about the same density as lead, is soft enough to shoot in anything, and I love it, but it is even more expensive than Hevi-Shot.
Have you tried patterning some premium #4 Buck? It has been a while, but I got real good patterns from Winchester 3" Magnum buffered Super XX buckshot some years back.
In my pursuit of the ultimate long range goose loads some time ago, I shot well over 2,000 patterns, and played with all kinds of barrel modifications and choke tubes. I found with large shot I got the tightest patterns with slightly less than Full choke. Unless you want to go with custom tubes, I would suggest trying an Improved Modified choke tube rated for steel shot. I have zero experience with the choke tubes advertised for Dead Coyote shot, so I can't tell you if they work well or they are just designed to get your money. I am real curious as to why they say not for steel shot, as original Hevi-Shot and Federal Tungsten-Iron were a lot harder than steel. Good luck.