Credit card and check payments in one order type
Seems like I was wrong about the 2nd order type.  Here's what I ended up doing:

I created a 2nd Order Type with the "Default, with Validation" workflow and a 2nd Order Item Type pointing to the new Order Type.

Then I used the "hook_commerce_order_presave" hook to change the order type from the default first Order Type to the other at the "review" step of the checkout.

Still, to me, this seems like a common enough occurrence (checks &amp; credit cards accepted in one store) that there should be a no-code solution.  If someone know it, please share!