Ryder here, from the Social Care Team at Shopify. Thanks for posting! It sounds like you're trying to have two sets of variants, is that right? That is, you would like to have variants for print and separate variants for canvas items. While this can only be done natively within the Shopify Admin by creating two different products, we can look at some other options!
Our Shopify App Store offers a selection of a few apps you can browse through that will allow you to customize your product options and, subsequently, pricing. Bold Product Options by Bold and Infinite Product Options by Hulk Apps are both popular apps for this function. Might either of these work for your business needs?
Hope this helps! Please let me know if there's anything I can clarify.