Interesting as I have An older Alpha Q and a new Moots fork. For me it comes down to brake set up. My Alpha Q CX20 was chattering pretty bad....pads had worn in and squared up to the rim causing them to grab more than modulate. I toed them a bit and it fixed the issue. This is the first place I would look to help the issue.
The Moots fork does have the option of the crown mounted cable stop, which will fix the issue as it moves the stop to the fork and removes the under the stem hanger which is the culprit here. We offer the crown mounted cable stop as an option in the Moots store: http://moots.myshopify.com/collections/forks/products/moots-carbon-road-forks
I personally run mine the "old school" way under the stem and have had no chatter issues when the pads are adjusted as stated above. Toe-in is key.
Let me know how it goes and please, let me know if you have any other questions.