Hi Nate,
You describe a common problem. And different string makers use different core diameters (and some use hexagonal core wire, so it bites into the winding for improved performance. And I too sometimes find that in a tuning such as DDAd I have to compensate the A string at the nut. Curiously, this is not on every instrument.
And I find that choosing string sets that operate at equal/similar tensions minimizes compensation of the saddle, as well as producing brilliance in each string that is in a similar 'brilliance envelope', so that playing a scale across all the strings does not sound different from playing the same scale on a single string.
I have a spreadsheet that computes string tension for sets of strings, given their operating pitch, string diameter and whether plain or wound. It turns out that the the fudge factor "k" needed to compute the tension of wound strings is very similar for most of the strings I've encountered (GHS, DR, etc.), so an average can be used for a given manufacturers' strings.
PM me if you'd like me to email the spreadsheet. Requires MS Excel. At present I can only supply it in Mac 64-bit word (Catalina OS and higher), but soon will have it available in the more widely used 32-bit word version. Either one should work in a PC Windows environment also...
