So, I get using the calculations to account for larger tire diameter, but wouldn’t that only come into play if trying to compare mileage to the dash display? If you are calculating based on miles driven between fill ups, then it’s straight division, otherwise, you are calculating based on what it should be, rather than what it actually is, no?
You have it exactly backwards. The mileage calculated using the odometer vs the mileage display should track each other, because the mileage display uses the odometer for its calculation. The actual numbers won't be the same because of other errors in the onboard mileage calculator, but they'll go up and down together.
However, our goal is to find out how many miles (each = 5280 feet) we can go on a gallon of gas. That requires us to adjust our odometer reading when we change tire size, because the odometer is off by the ratio of actual tire diameter to the stock diameter. As AuSeeker says, the best way is to calibrate the odometer against a GPS so you have an accurate correction factor. You can also use the mile markers on an interstate highway. Just go 10 miles according the markers and see what your odometer reads. In your case it will probably read something like 9.2 or 9.3 miles. 10/9.3 = 1.075 which is your correction factor.
The odometer effectively counts numbers of wheel rotations (actually numbers of drive shaft rotations). It has no other knowledge of how far you've gone. If your wheel diameter changes, the odometer reading will have errors.