swept reveal lip not merging with body

System:  Solidworks basic edition, 2012 X64

good morning,

I'm working on a part today that is comprised of two independent layers.  one that is going to be injected plastic, and a second overmold TPE layer.  This part, which covers an antenna, is intended to match up with a housing that is driven by a seperate master model (due to a difference in shell thicknesses that I can't reconcile)  Every feature with the attached part is a-ok, except for an overlap lip which supposed to run along the 3D curve that defines the power button area.

So far, I've tried to make a solid swept feature, using a fitspline as my path.  This feature does technically solve, but if you look at the filleted areas along the path, there is some bad surface blending that's happening.

I've also tried a surface sweep and using a thicken feature to merge the bodies together.  With this method, I can get the surface body up to the point where the bodies would need to merge together, but the thicken feature then fails.

Finally, I tried offsetting and extending surfaces into eachother to bluff my way into a lip feature.  The extended surfaces quickly became very ugly and I found my feature tree bloating up with far too many trims and little fixes.  There has to be a simpler way to model this feature correctly.

and this is where I turn to the forum.

If you end up taking a look at my part, I'm recommending that you hide the rubber overmold layer and roll the feature tree back to a point in the folder labeled "injected plastic features"  There you will see a 3D sketch and profile for the sweep that I'm trying to create.  Ideally, if I can just get a method for the creation of this lip in any method, I can re-work the rest of the model so that everything is ok.

Thank you for your time,

SolidworksParts And Features