I've done something a little similar, actually. We're restricted to a certain payment processor that has to be done after the fact - it's a long story, but that's the end result.
So, what I did was to make a new payment method (search google, a minimal one is actually pretty quick to make), and it does nothing really - no online payments, etc, it's just like the "check_mo" method that comes with Magento, I just did a new one so we could still use the Check/Money Order method later if we wanted.
Then, on the success.phtml template (this is the page that is shown at the end of the order, telling the customer the order number) I have a
<div> with the z-index set such that it covers the page entirely, and has an iframe to the payment processor, so it's at least somewhat painless to use. Since it's on the success page, I can pass along the order number so later on we can correlate the two things, and confirm that it's paid.
In your case, you could have it just be a link on the success page, or as you said, just put it in an email, etc.
In our case, the customer does still have to click on our payment method, but there's no information they enter in for it, or anything like that. That might be a deal breaker for you, but for us it was a nice compromise, since we still want to offer one or two other methods anyway. Sounds like something very similar might fit your case.