How do I get a three-way colour blend (and rounded edge effect)?

For what it's worth I'm using Illustrator CS5 but I imagine any solution will apply to all recent versions.
In practice I've pretty much got where I need to so this isn't an immediate problem, but I'm sure there are much better ways of achieving the effect and I'd like to have them in stock for future reference. I'm not sure if this is a basic matter that I should be able to figure out easily or a challenge for more advanced practitioners; either way, I'd be grateful for any suggestions.
The end product I was after - sort of - is shown here:
The two elements I struggled with were:
Blending the colours where they join - particularly the three-way blend at the middle, which in the end I avoided by placing another object on top! I resorted to a manual, tedious and inaccurate point-by-point approach using meshes and it didn't really deliver what I wanted, which was a seamless join between the colours.
Getting the effect of a rounded edge at the perimeter of the triangle - I used the same mesh-and-guesswork technique (and it shows).
In whatever solution anyone can suggest, one of the important things is to be able to dictate the distance over which the blend and shading operate, both where the colours merge and at the rounded edges. Feel free, by the way, to start from the very beginning with "First, construct your triangle" - I realised, as I did this, that there are a many different ways to do that, and one may be better than another for a particular blending approach.
Thanks for your thoughts,
Giles.

1. Polygon Tool: ShiftDrag to draw a triangle oriented with one of its corners at the top.
2. Apply a linear grad fill, blue to white, -90°
3. Appearance palette: Add New Fill. Linear grad, red to white, 30°
4. Appearance palette: Add New Fill. Linear grad, green to white, 150°
5 Appearance palette: Select each fill. Set its Transparency Mode to Exclusion.
6.Deselect. Select the path. Effect>Distort>RoundedCorners.
JET

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