Another way would be to just select the straps of your original mesh and then press P this will separate the straps from the dress creating a separate mesh. Apply the solidify modifier to the straps mesh only and apply, then delete the unwanted faces. Select both meshes again and press Ctrl+J to re-join. In edit mode select everything and press W and select Remove Doubles. So long as you didn't move either the straps or the dress during the steps I just described then the default tolerance for the Remove Doubles function should weld the duplicate vertices created when you split the straps from the dress. There may be a need to create some additional faces to fill some areas that the Solidify modifier didn't include depending on how you spit your straps from the dress. This way eliminates the need to export/import mesh objects as .objs.

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