I’m looking into the Shopify API for ways to update the pricing of a product on the fly depending on user input but not by having different variants of the product. So far, I checked the cart API but that is read only in terms of modifying the cart value and couldn’t see any straightforward way in the admin API.
I just wanted to let you know I have moved your query here to our dedicated API forums.
These threads are monitored and responded to by our own Developers and Partners, so it’s really the best place to look for API support, as we’re not able to provide that level of support ourselves directly here.