MB here. We pay our nanny an hourly rate plus overtime, calculated out to a weekly salary (at her preference). This is all negotiated in gross pay. We use a payroll service that handled our appropriate tax payments and her deductions as she chooses.
We do not "gross up" and I would never do that. I think our approach is pretty typical and think what your candidates are proposing is not the norm.
We found our best nanny candidates through neighborhood listservs and word of mouth, but agencies can be a good option, or care.com, mothers/parents groups, etc...
Good luck.
another MB here. We do the same.