Should I include independently derived but not novel results in my thesis?
There is usually no reason not to include something in a thesis.  Your thesis is a place for you to give a coherent account of all your work on a topic.  There are (usually) no page restrictions, and it should serve as a reference document for future readers.

Many theses include a lot of review material, beyond just what might be contained in a literature survey.  A thesis has to contain new material, of course, but it does not all need to be novel.  There can be a lot of merit in giving detailed explanations of known results, if the reader is not necessarily going to be familiar with them in detail.  A derivation that has not previously appeared in the literature (even if the final result is known) is clearly suitable for inclusion.