Magento 1.9 – Fix Missing PayPal Payment Method in Backend Order

Adding answer from above so that this can be marked as completed:

PayPal Pro was less than ideal - can't auto return for CC/DC payments

Switched to PayPal Hosted. It works ok, but with limited options for customising the experience at PP, it still has a detached feel about it. But that's a PP problem, not Magento!

When Check/MO method is used, the invoice is created post checkout once you've received funds for an order. There is a checkbox letting you decide whether or not to send the invoice emails when you create these invoices.

When the PayPal method is used and configured to use the "Sale" mode, these invoices are created at the same time as the order is placed because the customer is being charged upon order placement vs fulfillment. I.e. The credit cards are being both authorized and funds captured in a single transaction.

Magento does not send invoice emails (for any payment method) when a Sale/Auth & Capture mode is being used. If you were to switch to the Authorize mode, it would function pretty much the same as the Check/MO method in that you would have emails sent for invoices and also would have to create them upon fulfillment to actually capture the payment.