Just had another idea of for a new way of approaching this business. Another opportunity for you to tell me why I'm wrong...! ;)
For most businesses, same day delivery is an expensive fall-back option which they want to minimise as much as possible. In other areas of life we take out insurances to mitigate against risks (breakdown cover, home insurance etc etc) - so why couldn't businesses take out same-day delivery insurance cover?
Profitability would of course depend on the nature and size of their business, and the amount you can persuade them to pay monthly.