It sounds like your cross effect strip is being applied on top of the multiply effect strip.
The result of the effect strip completely overrides any strips below it. To work around this, use the cross effect strip to blend the multiply effect strip and the black color strip.
There are many variations on how to go about this, for example:
Add a Multiply effect strip with the image and the video strips selected.
Add a Cross effect strip with the Multiply effect strip and the color strip selected.
Add a Cross effect strip with the color strip and the video selected
Set the Blend of the image strip to Multiply in Properties region (N) > Edit strip > Blend
Add a Multiply effect strip with the color strip and the video selected
Add a black color strip on top and keyframe the Opacity in Properties region (N) > Edit strip
Without any effect strips:
Set the blend of the image to Multiply and move it above the video strip
Add a color strip on top and keyframe the Opacity.
Also see this question.