Not sure if this has a solution, or may even be a bug, but I wanted to see if anyone could help. B:2.79
Lets make an animation of 20 frames, using a single plane mesh. Animate the plane location along an axis from frame 10-20. It should be cloth while it's moving, so bake a cloth sim to the plane also from frame 10-20. Fine so far... But now the animation needs to be twice as long, and smoother - so lets change the time remapping. Leave the old value at the default 100, and the new value I'll make 200, and the end frame I'll set to 40 - so it's now double the length. Our cloth sim also needs to be adjusted, so I'll re-bake that from the old F10-20 to the new value of F20-40. This works perfectly on a static mesh.
But our mesh is animated, and now when the cloth sim begins at frame 20, the location of the mesh immediately jumps to frame 40 (its end location). So at frame 20 the mesh suddenly teleports from the start location to the end location - highly undesirable.
Side note: I've tried to export the cloth sim to MDD and import it as shapekeys, but no matter how many times I apply loc/rot/scale to the mesh the imported result is a garbled vertex mess. So I cannot use this as a solution. I'll also mention that in a very complex scene with multiple particle and physics sims, it's not so easy to just scale all the keyframes by 2.
Very interested to know of a solution, but would settle for knowing if this is a limitation (I'll get over it) or a bug (I'll submit it).
With my thanks in advance, C.