You can keep in the review summary simply by not performing Step 6 of the installation instructions.
The method that your listing would be much better, however it would be difficult to support as a mod because it requires some core code changes.
One way of doing it is to code it to skip the payment options page, and move forward to the payment page with the default credit card options page, edit the page to also display the order summary, and include an additional form submit to alter the payment method.
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