One trick I have found when trying to CL a perimeter that is conjoined with other entities in the model is take a copy of the perimeter and move it (on an axis) out away from the model.
That makes it far easier to edit out anomalies that prevent the mesh from forming. You can also simplify the perimeter by deleting 2 adjacent short lines or deleting fragments and make one endpoint to endpoint line in their place.
Then you can create the surface without problem.
After which move the meshed group back to the model along the axis and cleanup the model where the lines should meet the surfaces endpoints.

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