Non linear editors are generally not used for compositing for a number of reasons. NLEs have very thin margins for performance, while compositing may require hundreds to thousands of operations to craft a desired output. In industrial imaging, these two processes are isolated and divided for this very reason.
While you might not be doing post production on a feature length film, there is much to be gained by following the patterns that such projects follow.
- Cut your project into the shots and timing you require using an NLE. Once you are happy with the pacing and the edit, your edit is "Picture Locked." You now know precisely which frames you are going to be performing deeper surgery on and what elements you require.
- Take your work into the compositor and perform the surgery. You gain the added quality of compositing on 32 bit float imagery as well as avoiding other not-so-obvious compositing problems such as nonlinear color blending. Specifically regarding your work, you can find various tools to help you regarding motion blurring. See Motion Blur option in the mask nodeMotion Blur option in the mask node.
- Repeat for each shot required. At the end of the process, output your still frames and encode to a final motion picture format if needed.