Excel - How to calculate gross amount when you know net amount after taxes but need line item detail

Hi all,

Trying to figure out how to calculate the required gross amount for a financial distribution when I know the net amount and individual taxes.  Can't use the normal grossing up formula of 1) Adding up all federal, state, and local tax rates, 2) Subtract the total tax rates from 100%, 3) Divide net payments by the net percent:  Net Payment / (1 - total taxes) = Gross Payment, because the state tax needs to be rounded to the nearest whole dollar.  In this situation I would personally use Solver, but I need to roll this out to team members who don't have Solver so that is not an option.  

Here's the example:

Thanks all,