Use a split line to project the text to the surface then you can turn the split line into a surface and thicken - then delete the body..
Any chance you could upload the part file? If the part is proprietary could you make a similar part that has the same problem? I have found that solutions are found much faster if people can access the file and play with it. Also, it looks as though you are using the surface extrude function try and use the surface thicken command or surface thickened cut, after converting the sketch to a projected sketch like John suggested.