Ok, this can be done using
Sketchup, Shapeways'
Create 2D to 3D, Netfabb's
Cloud Service and Netfabb's
Studio Basic.
First install Sketchup.
Then install three plugins for Sketchup. An STL importer called
Sketchup-stl. The instructions are
here. A deformer called
Shape Bender and notice in the instructions it calls for installing
Progressbar.rb.
Then install Netfabb Studio Basic.
Having done that the workflow will go something like this. Check the design rules for the
material you want to print in. Then design your 2D design in Illustrator or whatever 2D vector graphics software you use as you already have and then make a separate file that will be your elliptical background. Upload and extrude both of those files using Shapeways' Create 2D to 3D. Then go to your My Models page here on Shapeways and download them. Click on the text to go to the model page to download, not the edit model link. This will get you the two STL files you'll need. You can avoid this step if you find out how to import AI files into Sketchup. I skipped doing it this way cuz I'm not sure what's a good way to do this.
So now import the two STL files in Sketchup and use the Shape Bender plugin with some curves that you draw with the radii that you want. The scale should have been picked up from the STL file that you made with Shapeways' Create 2D to 3D. If you want to know how to do just about anything in Sketchup just search Youtube as there are bajillions of tutorials on there for Sketchup covering just about everything you would want to know. Once deformed, position them how you want with a little intersection between them. You need to have them intersecting a little so you can weld them together. After everything looks good in Sketchup export it as a single STL.
Now take your STL and upload it to the Netfabb Cloud Service to weld everything together and delete all of the unwanted polygons inside. What The cloud will give you is a perfect watertight STL that you can upload to Shapeways. You can do all of this in Sketchup, it's just easier to do it with the Netfabb Cloud.
One last step is to import it into Netfabb Studio Basic and double check that it is the size that you want. If it is you're all good, if not use this software to adjust the scale. Now all you have to is upload to Shapeways and pick the material you want to print in.
Let me know if you get stuck and we'll sort it out.