It's done by neighborhood, not zip code. You can look up the address at
https://otr.cfo.dc.gov/page/real-property-tax-database-search to find out the neighborhood. You could call DCHA to see what they'll pay for that neighborhood--I wish I could find where it used to be written down!
DCHA won't let you use a voucher for a place that costs more than their standard, even if you're willing to pay more. So the landlord will probably either reduce the rent to whatever DCHA will pay or keep the rent where it is and rent it to someone who doesn't have a voucher.