However, NH’s property tax rate more than makes up the difference. Property taxes don’t care what your personal income is whereas taxed income often has some relief in the form of deductions or exemptions.
You don’t have to own a home in a state to use it as your official residence. Heck, just look at how many members of Congress get away with renting an unfinished basement in a friend’s home back in their home district and using that as their “residence” even as they own and maintain a residence in D.C. or northern Virginia.
Another option is to have the S Corporation own the home in a state like New Hampshire. The taxpayers can then pay a nominal rent to the S Corp. for their own home. This allows them to take more deductions on the home (depreciation and repairs, for example) than they would be able to take as individual taxpayers.