I agree with your analysis, however, I believe that Ginsberg would be firmly on our side. Ginsberg (with Breyer) wrote the dissent in Smith v. Doe saying:
“Measured by the Mendoza-Martinez factors, I would hold Alaska’s Act punitive in effect. Beyond doubt, the Act involves an “affirmative disability or restraint.” 372 U. S., at 168. As JUSTICE STEVENS and JUSTICE SOUTER spell out, Alaska’s Act imposes onerous and intrusive obligations on convicted sex offenders; and it exposes registrants, through aggressive public notification of their crimes, to profound humiliation and community-wide ostracism. See ante, at 109, and n. (SOUTER, J., concurring in judgment); ante, at 111-112 (STEVENS, J., dissenting in No. 01-729 and concurring in judgment in No. 01-1231).
Furthermore, the Act’s requirements resemble historically common forms of punishment. See Mendoza-Martinez, 372 U. S., at 168. Its registration and reporting provisions are comparable to conditions of supervised release or parole; ”