Does cloth work with the time IPO curve?

Hi there,

I’m trying to get a slow-mo cloth simulation rendered (real slow-mo, without frames duplicated by the VSE). For some reason when I use a straight timecurve on the cloth, it seems to slow down and speed up unpredictably.

Blend (without textures) is at:

Does anyone have any ideas why the speed would change like that, even with a straight time curve? Is there any way around this? Have I done something obviously wrong here? Any help appreciated!

Note: The first 15 frames are at normal speed, to get the cloth ready. The spinning cube uses the exact same time curve.