oh, his birthday is june 7th, and a monday this year?
last year, his birthday was a sunday, and Nanami's was october 2nd on a friday (he came to her house on a thursday). this eliminates 2015-2016 as a prospect (sunday and tuesday) and puts the current year as either 2010 or 2021. if course, I probably could have just remembered that the switch came out in 2017, but eh.
given their ages, that Puts Kaoru's birthdate as July 7th 2004 and Nanami's at October 2nd, 2003