I think that your suspicion that the difference is related to how the tax is calculated is correct. I believe some states tax only the monthly payment, some tax the entire total lease payment up front (meaning the tax must either be paid upfront or rolled into the amount financed), and a few states actually tax the entire capitalized cost up front (which it looks to me to be happening in the dealer's calculation). I don't know what your state does, but get that straight and you will probably have found the issue.
dd: 2014 X1 xDrive 28i MSport
in garage: 2011 Mazda MX5 Miata 6mt
Wife's car: 2012 X3 35i
2008 328i 6mt
2005 325i 5mt