One way would be to use a Planar Mill operation, set the boundary plane at the height of the curves. Set the floor at the desired depth. On the cut levels you can set Incremental Side stock. this way you can get a tapered tool path
I cannot download files so I could not look at what you had attached.
Your on the right track...
I would use planner mill, not planner profile
Describe the tool as a chamfer mill,make sure the descrition... (taper, tip dia. are correct)
Bounday face is the top/sketch plane. Pick the line boundary as an open profile (tool on the correct side)
pick the slot bottom as the floor. Set your cut pattern to profile
That's all you want one profile pass following the sketch curve. that is what you will get. toll will contact the correct spot on the curve... tool taper driving on the curve edge
Works great for edge chamfering too. set the floor where you want the tip of the tool to be, set the stock as minus stock and you get nice edge chamfers.