I have to say I agree with the PP.
I'm a nanny, but many of my friends are moms who employ nannies and those who pay under the table are not willing to pay above board without a serious pay cut (they are paying their maximum already, so taxes on top of their nanny's gross pay wouldn't be possible). You either need to find a new family who's willing to pay legally right off the bat or ask your employers to make the adjustment sooner so you don't feel like it's such a painful loss in a year.

Sorry OP, it's no good all around.