I do not have access to the formula that you have asked for but if you are using paper load & trim sheets and they are anything like the 737 ones, it should be possible to convert %MAC to Index units using this.
Just plot the new Dry operating C of G position using the weight and the % MAC. Then drop a line vertically down or vertically up to the Index Scale. Read off the new DOI where this vertical line crosses the Index Scale.
If you know the Dry Operating weight, % MAC and DOI prior to the recent reweighing, you can test the validity method using the data for the previous figures.