I have reached out, just now, please begin the discussions with us asap because we are in the middle of going with Emburse and would consider this instead.
Emburse are great! They provide far more in the way of user a user experience to set controls, manage budgets, etc. We'd highly encourage going with them! (Stripe Issuing is an API-first product -- if you want to build software like Emburse, we would be more suitable.)
Roger from Emburse here. We're built on top of Stripe :D