When you run a camera track AE calculates the focal length and position of the camera based on the perspective changes that happen to the fixed geometry in the scene. A 4K shot has a bigger frame size than a 2K shot so the focal length is going to be different but the camera position is not. The problem is that the focal length and angle of view depends on the frame size of the comp. This means you cannot simply copy the camera and paste it into a bigger comp.
Fortunately there is an easy solution. Let's say you scaled down your footage 4K footage to fit in a standard 1920 wide HD comp. The height of the comp doesn't really matter, we're only concerned with the width. This same technique would work if you rendered a 1920 wide DI (digital intermediate). If you just scaled the footage to fit horizontally in a smaller comp you would need to pre-compose moving all attributes before you ran the camera track on the pre-comp. If you rendered a DI then you would just camera track the footage.
Now camera track is done and everything works just fine. You've inserted your nulls or solids and exported the comp to C4D and created your 3D scene and all is right with the world.
To replace your footage with the 4K footage and fix the camera solution you would simply run the Scale Comp script that comes with AE. You open up the comp and then you type in the width of your 4K footage and press go. Everything is done for you. You now replace the scaled up pre-comp or scaled up DI with the original 4K footage. You export the new comp to C4d and you import the smaller animation into the new C4D comp and scale everything up to fit. The C4D part of the pipeline is the only part that requires some calculations. Everything else works.
I hope this helps. I have been doing this kind of thing for about 10 years and the File>Scripts>Scale Composition.jsx is exactly what you need.
Thanks a lot for this detailed breakdown sir; much appreciated!
Your wisdom and experience shared here are indeed unique.