How can I use both radio buttons and checkboxes in the same payment option block?

The first two items shown as checkboxes here are mutually exclusive, but I am not sure how to make them radio buttons instead of checkboxes. The only option I see to add radio buttons places a new module outside of the billing feature (something that seems to be only concerned with collecting information, but not adding to the cumulative product total for billing purposes).

It's not possible to do that with the integration while selling products, but you may use the basic check box and radio button fields to display your products and then perform the calculations and pass the result to the payment field. 

Here's an example about it: https://form.jotform.com/73617144345961 

Now, these guides will help you doing so: 

https://www.jotform.com/help/301-How-to-Assign-Calculation-Value

https://www.jotform.com/help/259-How-to-Perform-Form-Calculation-Using-a-Widget

https://www.jotform.com/help/275-How-to-Pass-a-Calculation-to-a-Payment-Field 

I hope this helps.