Is there a way to use my.tokens on landing pages that exist in the design studio? We have certain landing pages that are used for multiple campaigns so I don't have them tied to any specific program. That's why I opted to create them in the design studio but I don't see a way to use my.tokens if my landing pages live in design studio.
No, there is no way you can do this, as by definition, my tokens belong to programs and they belong to Marketing activities.
You may wan to consider using Snippets instead. In some situations, that works well: Add a Snippet to a Landing Page - Marketo Docs - Product Docs