The easiest analogy is movie clips as in Flash. I figured I could render out an animation and use that as a material on a plane somewhere so that there would be two objects separate from each others timelines, but the fps is seemingly not allowing independence.
In other words, whatever the main project render settings are, specifically the fps, that's what everything is running as.
Can I get something like two different timelines in one project?
Not sure you can do that since everything is based on the documents FPS.
Understanding your flash analogy from when I use to use it another way is to use Xref's which has is essentially importing another scene into another. It has it's own control for it's animation somewhat but it's still based on the scene that it's in so you would have play a lot with it and might have a similar problem I think.
My suggestion would be to use a after effects with cinema 4D. C4D exports a file that you could import into AE then using a external composting tag and a object buffer to mask the area on the plane. You could place any image or video on the plane and control and remap the timing easier in after effects then in cinema 4d.