Help with converting edges to curves

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Hey guys, I have what I think may be a simple question, but for the life of me I can't figure out what to do about it. I have the following mesh (picture attached), and I want to create a smooth curve along the selected edges (highlighted in red).
My first thought was to select the edges I needed curved and then do Modify/Convert/Polygon Edges to Curve. However, upon using this, while I can see the smooth curve Maya created, it did NOT replace my low poly curve and therefore the smoothed curve is just floating above my old one. I have since tried other methods, but none have come as close to working as "Polygon Edges to Curve." Am I doing something wrong, or is just impossible to create a smooth curve from a selection of edges? 😕
Any help would be VERY much appreciated!
- John