Create an alternate Stripe Payment Method
A no one has come forward and told me it's a bad idea, I've ploughed on and done the following:

Created my own Controller action in my plugin to bypass the payment side of things altogether. I didn't use Omnipay to create my Customer on Stripe in the end. I went with using Stripes own API directly as documented here.

To complete the Order (as-in convert a Cart into a full-blown Order, it was as simple as calling the following Commerce method:
craft()-&gt;commerce_orders-&gt;completeOrder($cart);