To the petitioner, do you see the case of Wooley as pertaining to speech by public entities?
At the very least, in this case, yes.
In the example I gave when I submitted my brief to the court, I described a situation where individuals were being forced to pay for a motto to be affixed to their school district's buses. One that they had moral objections to. One could argue that, by forcing this, the regional government would be breaking this precedent set by Wooley, as although the individuals do not own the school buses themselves, it is property they paid for.
If one finds this to be an overly broad interpretation of the ruling, I also assert that this law has issues in our system of federalism.
The regional government is coercing localities to display their message. Such an arrangement goes directly against the idea behind the ruling in Wooley.
The State's second claimed interest is not ideologically neutral. The State is seeking to communicate to others an official view as to proper appreciation of history, state pride, and individualism. Of course, the State may legitimately pursue such interests in any number of ways. However, where the State's interest is to disseminate an ideology, no matter how acceptable to some, such interest cannot outweigh an individual's First Amendment right to avoid becoming the courier for such message.
It is reasonable to say that similarly to this situation, the region's interest cannot outweigh the locality's rights to avoid becoming the courier for their message.
But understanding that all actions of the state are in some sense paid for by taxpayers, would that then imply that expressing ideological stances is a power that does not belong to the government?