Help my businesses find a merchant account or payment gateway

I have 2 different businesses that have a *very specific need* to process cards. Both are offline legitimate businesses, one is brand new with no history and one has 1.5 yrs of history with financial records, etc. Our specific need is that we need to locate either a merchant account or a payment gateway that is able to process transactions using the 6 digit pre-authorization code. An example of this kind of transaction can be seen in this article [login to view URL] We are fine with either a merchant account with a physical terminal as long as it can process keyed-in transactions this way, a hybrid service that has a terminal and a web gateway, or an online only gateway. Most of popular online gateways like Square, Stripe, and PayPal DO NOT have this capability. We need an expert in this area to help us locate which processors will fit this need.