[EL] First Amendment & ballot pamphlets

Candidates for municipal office in San Francisco (and I assume elsewhere in California) may submit a 200 word "candidate statement" for pubication in the official, state-issued voter guide. The candidate can say whatever she wants, subject to two limitations: (1) the candidate may not claim the endorsement of a group or individual unless she also submits evidence of the endorsement, (2) the candidate may not "include [in her statement] the party affiliation of the candidate nor membership or activity in a partisan political organization."

The latter restriction was presumably intended to preserve the "nonpartisan character" of formally nonpartisan municipal elections. It seems to me, though, that it might be vulnerable on First Amendment grounds. Does anyone know of any First Amendment case law regarding restrictions on what may be said in state-issued voter guides? Or have an otherwise-informed opinion about whether this sort of restriction could survive a First Amendment challenge? (Is the state interest in maintaining the "nonpartisan character" of formally nonpartisan municipal elections strong enough to bar a candidate for mayor or city council from making statements of partisan preference or endorsement in a fora created by the state for voter education? Might the answer depend on evidence regarding (1) the degree to which the major party brands have "meanings" specific to the municipality (so that they're actually informative regarding candidate positions on local issues), and/or (2) whether there is a severe imbalance between the number of Dem and Repub voters in the jurisdiction by national party ID (which for various reasons may impede the development of competitive party politics at the local level, or even make the competition pointness)?