Dave;
If you study those old powder & shot dippers, you will note an error in their markings. "Most" though not all, have the same setting for various amounts of shot & poeder. shot is normally marked in 1/8oz increments & powder in ¼ dram increments. At the 1oz setting for shot the powder normally reads 2½ drams. This is pretty accurate, however if it goes far enough to double the capacity (I have one which does) to 2 oz, the logically the powder should also double to 5 drams, but recall it has gone up by 8 ¼dram increments so arrives at 4½ drams instead. Each change of volumn equal to 1/8oz of shot actually changes the powder charge by about 5/16 drams, but most measure are not so marked. I do have a little Lyman dipperich does not have the preset notches, but is simply set to a line by friction. Shot markings are on one side & powder on the other. The lines do not co-inside as the do on the majority of these dippers, so would seem to give a more accurate reading of the actual powder drams. Most that I have checked seem to be pretty close on the amout of shot dipped. By simply using the same setting for dipping Black the charge will be a good one, though may not be just what the measure says it is.
Ted; As best as I can recall I can't think of a single game bird or animal which I have ever killed with a Square Load. I have simply never hunted with any of the following, .410 = 3/16oz, 28ga = 9/16oz, 20ga = 5/8oz, 16ga = 13/16oz, 1ga = 1 1/16oz or a 10ga with 1¼oz. With only minimum rounding those are esentially the Sq loads for the different gauges.
Much more important is a load balanced to the size of the bore, in relation to the desired shot charge & burning rate of the powder. This can of course be done for any conceivable size of hole down the bbl within the range available burning rates of powder at hand. Irregardles of the gauge one should load a lighter charge for Red Dot than for Blue Dot etc.

PS; I suppose you are aware that if you put a 1 5/8oz load of shot in a 20ga it would have a shorter shot column than 3/4oz in a .410. The normal 1¼oz load for the 3" 20 is only very slightly longer than the ½oz .410 load. Ever wonder why the .410 is normally loaded with rifle powder rather than shotgun powder?

Miller/TN
I Didn't Say Everything I Said, Yogi Berra