Multiple Draft Angles For Embossed Element on Complex Curved Surface

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I'm pretty new to Inventor, having recently moved over from Fusion 360, where I'm at an intermediate level. I have a challenging problem that I'm not sure how to accomplish.
Problem:
I am preparing a model for injection molding, and the part is going to have a logo embossed in it. Because of the way the part is made, it needs to have a draft angle just off of the vertical axis. However, because the logo is oriented ~30 degrees off the vertical axis, this results in a sharp edge and concave hollow on the top of the logo.
Here is the base part I'm working with:
I need a way to create multiple drafts on the embossed shape, so that the bottom edge of the embossing extends down to the part surface vertically, and the top edge extends to the part surface horizontally. In this image, I have drawn the two draft angles in blue and red, with an approximation of the intersection with the base part drawn in green:
The part is a revolved shape, not a simple curve, meaning that I can't use regular embossing methods. My solution was to split the surface of my target body using the logo, and then use the thicken function to create an emboss.
However, now that I've done that, Inventor won't let me modify the drafts of of my shape. I get the following error message when I try to apply a draft to any of the faces:
I tried sweeping the Logo solid, but I get an error message with that too. I'm not sure what to try next.