Making a decorative border

So I am making a 3D printed night lamp for my daughter.
It will be her name written in a cursive decorstice font using 150 mm high letters extruded to 60 mm depth and offset so that there are a few cms to put a LED chain light in there.
I want to print a cover for the space between the letters and its supposed to have a decorative edge.

I already printed the body and a prototype of the cover but its supposed to resemble a cake with the cover being a glazing that runs down the side in drops every few cm.
This is the decorative border I am struggling with.
I can not get it to work with project since it wont do it on the backside and even when it works most often I cant extrude or offset face and it gives me error messages like "resulting body wouldnt be valid.

Here I am testing it and that is the printed lamp body + cover prototype

Please help me.

Hi Matthias,
You could try making another body that is larger than the cake, but follows the same contour. Make it a shell, so it is as thick as you want the frosting. That would be the frosting layer down the side of the cake. Then you can add a construction plane(s) then sketch a face of the “un-drippy” frosting (where you just want cake). That face could be extruded and when you go into the frosting layer, it will change to subtracting, and cut away the frosting you don’t want.