Moving Cloth Simulations on the Timeline

I’m working on an animation that involves multiple cloth simulations to show multiple theatre curtains opening one after another. I have the individual animations baked fine, but I was wondering if it’s possible to move them around the timeline without re-baking them? It’d be nice tune the timing without having to do a 5 hour bake each time I shift it a couple of frames…

I tried converting the simulation to a shape key, but that only saves the endpoint, not the whole simulation.

That worked perfectly. Thanks!