Hi,
The PHP variables initialized on that view are not and can't be the same as on the checkout so just copy / pasting code from the checkout there cannot work.
The checkout views are made to handle a cart. On the pay view, you don't have a cart, you have an order. So if you want radios there, it requires proper PHP developer in the pay view to display the radios with the correct HTML based on the variables available.
There is no setting to have the pay view display the payment method selection as a radio list. Why you ask. That's because we never thought about it and no one brought up the subject until now.
Why we made it as a dropdown there ? That's because it looked better than with a radio list since the dropdown is aligned with the total. With a radio list, you would have the total on it own below the radio list, which we figured would be less nice.