Pied Piper -

A couple of manufacturers make "white bronze" wound strings that might give you the marker color for the the white strings with minimal difference in string properties.

For all practical purposes, the optimum tension of the string is determined by the size of the core wire, and the manufacturers won't tell you directly what that is. If you really want all the strings at equal tension, the they will all have the same core wire diameter - regardless of length.

Most instruments I've looked at string to about 30 pounds per string, which means they all have a (steel) core close to 0.011 to 0.016, since that range gives good stress levels.

The winding adds the weight needed to bring the pitch down to whatever you want, but doesn't contribute anything to the "strength" (indirectly the tension) of the string. Bronzes of various kinds are the common winding materials, although a lot of things have been tried. The density of available bronzes can vary over a fairly wide range, so the "wound diameter" isn't a very good indication of the actual weight (pounds on the scale) of the string - unless you know more than the string people like to tell you.

Differences in core diameter of as little as 0.0001 inch can make a significant difference in the string stress level, and the "guages" are rounded off rather crudely. In addition, nearly all strings are plated or otherwise coated with something, and since the platings go on "annealed," they don't contribute much to the wire "strength" - so a "very accurate" actual measurement of the finished wire diameter may not tell you too accurately how big the "core of the core" is.

John