radial grid projection fails when source surface is smaller then the grid

Hi, this is my problem:

I am trying to project a radial grid onto a surface using the map to surface battery (and then try and produce something from there).

When i build a rectangle using bounding box> deconstruct box> rectangle it fails,

When i build a surface in rhino that is bigger than the radial grid it works!

But when i make a surface that is smaller than the grid (like in the file added, data is internalized), and the curves in the edges go crazy, and i only want to project a quarter of a circle on to the target surface! what can i do?

P.S.

Is there a cleaner way to thicken my result other than weaverbird?

thank you! 

Adi