Use billing schedule as variation attribute

Problem/Motivation

Hi,

I sell a subscription to a numeric product. Customers who buy this subscription will be able to use the product for one year. I want them to choose between paying 120€ every year or 10€ every month (for at least one year) for the same product.
Thus, I created two billing schedules (for yearly and monthly payments) and two variations of the same product, onne for each billing schedule.
My problem is that the add-to-cart form of the product doesn't show a select input for the billing schedule, as it would do for a standard variation attribute. The only way I found is to create a "payment frequency" attribute, that doubles the billing schedule field in the variation : it doesn't seem a clean way to do.

Any suggestion ?

Thank you for your help