First of all, you should correct both splines... the small segments on left and right ends are not correctly modelled. If you move one vertex, you will see what I mean.
Than attach both splines together, use cross section modifier, and then use surface modifier (threshold should be below 20).
I then used edit poly modifier to correct geometry at ends where those small segments were... simply delete polygons an bridge edges.
As far as mapping this thing goes, I would use spline mapping method, probably best to use one of the middle edge loops for that.
Hope it helps
