I disagree. I think Cara Red makes a very red beer. You do have to use a lot of it, but it seems to be more fermentable than other crystal malts. But in a good portion it gives a deep red color. I don't have my recipes right now in front of me or I would give you the percentage.
+1 on the CaraRed
A little body will help this beer stand out as something unique rather than a hoppy wheat beer with coloring. It will offset the spiciness of the rye and the citrus punch of the hops.
From a malt flavor standpoint, you don't stand to gain much from the Melanoidin in this recipe. A better bet would be to split the base malt with Pale and Munich. This will make the malt profile less "muddy" and allow it to simply complement the hops, wheat, and rye.
Sounds like a great concept! Let us know how it turns out!