Wind noise and 5DIII video

I'm using the hotshoe for an arm to place a Hoodman over the screen to address visibility in sunlight.

So, I'm trying to get buy with the 5DIII mike taking video.

Of course, I'm having problems with wind noise.

Any suggestions for a cover of the 5DIII mike? Has anyone tried anything that dampens wind noise?

If a sock works on an external mike, I'm wondering if something similar would help.

If I don't hear from anyone I'll try to experiment.

Thanks.