Do not complicate your life:
As mailing addresses and car registrations were not changed, there is no need to add evidence to the contrary and possibly raise question marks.
As for the continuous residency requirement, the evidence you have (deed to house, mortgage, taxes) is more than sufficient.
If asked during the interview why both of you were absent, simply explain your attendance in the program and that you did maintain residency in the state - have evidence on hand to attest to that fact is asked.