Separate, simple DTOs will make your life infinitely easier. It will require more code, but it will be boring, simple code, that is easily tested, and allows your interfaces to change and evolve independently.
Make a DTO for each request endpoint and a separate DTO for each response. Otherwise, you will eventually be sad.
If you find elements that are common to multiple endpoints, extract them into their own object, and include them in both.
And yes, using inheritance here would be wrong. Stick to compositional patterns and you will be fine.