An assembly includes a plurality of seal shoes arranged about an axial centerline in an annular array. The assembly also includes a seal base and a plurality of spring elements. The seal base circumscribes the annular array of the seal shoes. A threaded base aperture extends axially through the seal base. Each of the spring elements is radially between and connects a respective one of the seal shoes with the seal base. The spring elements are formed integral with the seal base and the seal shoes as a unitary body.