Whose #4 load are you using? The federal load made for the Judge is the best #4 load I've found - the shot is harder and their wad makes a tighter pattern than just about anyone else's load. The regular Fedal blue box #4 load is just as mediocre as everyone else's #4 load in the Judge. See the Federal "410 handgun" #4 shot box at this link for what the box looks like:
http://410handguns.com/410_federal_ammunition.html
Most of the info in the steel -vs- lead atricle I'd say goes out the window with a judge. Its forcing cone and barrel don't compress anything -- they are larger than the normal .410 bore shotgun (e.g. .451 -vs- .410). Shot deformation doesn't affect Judge patterns, its the darn rifling in the barrel.
About the only payload you can do for .410 is 1/2 oz. Steel would weight less, and I've never seen load data for .410 steel. You need to follow the load manual and a too short or too long shot column won't allow the crimp to be correct.
#1 steel is going to penetrate about the same as #4 lead. The performance of #1 steel -vs #4 lead is pretty much the same. Steel is harder, but less dense, and density is what you want for penetration in flesh. But #1 is larger than #4 so that makes up for the lack in density. You will have less pellets in a #1 load than a #4 load however.
Pattern density is another problem. As the range gets longer, the pattern opens up greatly, especially from a Judge. Smaller pellets mean more hits, but each hit has less penetration. You need to see what the problem is with the rats -- poor hits, or poor penetration. I would think a #4 would penetrate just fine on a rat at 10 yards unless these are the huge one the size of a shoe box.
If you want better performance, try heavishot (there are different densities of heavishot and I think all are more dense than lead by some more so). Heavishot is also harder than lead but not as hard as steel. Heavishot #4 or #5 may be what you need. But what you really need is the wad Federal uses in this #4 410 handgun load as I cannot duplicate their patterns in my handloads. You could also try a .444 marlin case as it will hold more shot (and try with and without a wad). But you're on your own for load data.