So glad I asked. All signs point to the traffic islands on Glendale still being called a national park. And, what's more, the Jamaican restaurant I've been looking for turns out to be TiGeorge's, and it's Haitian, not Jamaican. A reader named Sue wrote:

Take heart! The Islands of LA National Park sign is now on the tiny triangular island at the intersection where Allessandro angles to the right off of Glendale Blvd. southbound, by the motorcycle shop, before you get to Berkeley.

Re: the Jamaican restaurant. Are you talking about TiGeorge's? If so, it's way down... [south] past the 101, on the right hand side as you go south (in the middle of a bunch of other stuff). They make a fine bbq chicken on a fire right there, as well as a few other Carib. dishes. Yummy plantains. Goat, allegedly, on weekends.

Then, according to Pat Saperstein, a senior editor at Variety and an L.A. food blogger who describes herself as someone who "enjoys little tiny crunchy fish with sparkly eyes, mango drinks with frog ovary sacs":

You mentioned a Jamaican restaurant...are you thinking of TiGeorge's? It's farther south, at 309 Glendale Blvd., and it's Haitian. The chicken is definitely good, and so are some of the sides.

And, again, the national park: a reader named Peter gave these directions to the sign:

I've recently seen the sign (or another sign) at the little island where Allesandro breaks off of Glendale (just south of Effie St.). Jamaican food in Echo Park?

Now I know where to find TiGeorge's, and I'm looking forward to trying it. But why the sign moved, that one swims in the national pond of the unknown.