Here is what I would do in this instance: Assuming you only want to slow the speed down, and keep your motion just as smooth: right click your composition and choose composition settings and change your frame rate per second higher. For instance if it is at 24 fps change it to 96fps. Hit apply
After that, precomp your entire workflow, right click the precomped layer, and use time stretch and then change the speed by a factor of 4. (100% to 4000% for a 24fps-96fps rate) This will lower your frame rate back to normal, keep all of the detail, and allow you to slow it down.
The reason why this works best for your initial request is because you are basically doing what high frame rate cameras do, adding more frames and then playing back at a normal speed.
Here is what the other effects will do. Time remap allows you to set keyframes to slow down then speed back up motion, allowing for Bezier curves etc.
Timewarp reuses pixels in each frame to create a slowmotion effect (more used for video).
TROUBLESHOOTING: If the first technique didn't work, double check that any other precomped layer has the same frame rate as the main comp. That should fix any issues.