Just my stab at it:

If you use just the un-closed curves making up the major profile. (I used Trim to cut your loops, so that I would have just the top side.)
You can Network mesh those. I did this and then I aligned the top three points on the mesh because the top was too pointy.
It may be necessary to do some manipulating of the mesh points also.

If you incorporate mesh curves in-between the top ridge curve profile (length) and the side flanking profiles, and if they represent where your mesh will be at those locations - or in other words: add some quarter profiles, you'll get a more accurate shape.
In the photo (looks like a chicken drumstick), I see that the side profile seems to have a more squared out (or conic) shape, while not being completely round.

You could also then use Boolean Trim to flatten the bottom if you wish.



You can still also try the Sweep function. In the following example, I used the straight line in the middle bottom as the Rail.
And you can see the profile shapes positioned along the path. For an added measure of control, I used a Scaling Rail (top middle).

I also tried adding two side profiles on the bottom and used the those two instead of the straight middle line, adding more control to the shape.