Is there a better method to add uniform thickness to a curve pattern that has been converted into a mesh? I have the following mesh with no thickness or faces:



I wish to be able to apply a uniform thickness along with clean geometry without creating too many vertices.

The solidify modifier isn't getting me what I desire:



The skin modifier is getting me closer to what I want, but I am unable to control the thickness of the object, generating extra geometry from what I need and creating undesirable faces and edges.

The process here is after the skin modifier is applied, the geometry is flattened on the Z axis, vertices doubles removed, and then extruded. 





There has to be a simpler, less computationally expensive and more flexible solution to this that I am unaware of.
Maybe there's a simpler way but you could try with the Wireframe modifier:


Select your mesh, fill with F.
Give your object a Wireframe modifier. Enable Boundary, choose the Thickness you want.
Apply the modifier.
In Edit mode, select all and flatten with a SZ0.
Remove doubles with a W.
Delete the unwanted faces.
Work the angles.