Attribute Transfer

I'm attempting to link attribute data from sewer structures (Points) to sewer lines (Lines). The sewer structures have known elevations and the sewer lines are connected to said points. The sewer lines have attribute fields "UpS_Z" and "DnS_Z". I want to utilize the structure elevations to populate these attribute fields based on what is upstream and downstream on the sewer line.

I attempted to utilize the Attribute Transfer Mapping utility, but this does not seem to allow me the distinction I need.

Thanks!