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I think this should be correct:
since tire circumference is directly proportional to outside tire diameter, the ratio of "new" diameter to "current" diameter will be the same as the speedometer change, and the same exact ratio change is what you get for final differential change.
E.g., if 25.65" dia gives accurate speedo reading, the 27.69" dia tire will be 25.65/27.69 = 0.9263, so 7.37% lower speed reading. If you have 4.10 now, you will have 4.10 X 0.9262 = 3.80 diff ratio
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