Unfortunately, there is no way to have the clean version (devoid of dead verts/faces) and keep face order. The previous implementation deleted the faces from the mesh that you see, but they still existed in the data--and because they still existed, face order was preserved. In the update, the dead faces get cleared--meaning that face IDs that are deleted get filled with previously higher face IDs. There is no way to avoid this.
A workaround is to use the older implementation and clean at the end. But the current implementation is the correct way it should be done so I will keep the current logic in the modifier. It's unfortunate this affects previous usage that has topology-dependent modifiers above, but I didn't notice the issue until you posted about the issue. My habit is to avoid using topology dependent modifiers whenever possible--and the situations I built this for didn't highlight the issue in my own usage.
