"although this is getting looser all the time"
Apparently not. I queried this with Historic Scotland last year and was told the same routes that are always closed on a Sunday are still closed, and the same routes that are always open on a Sunday are still open. Worth chasing them again, though I don't think we're ever going to get the lovely idea of a park being a park through to Historic Scotland.
I'll not be here that day, as I may have gone along - though I still think it's a bit cowardly of the council only allowing this to take place in the park, on roads that for the most part are usually closed anyway. I mean, they have big running events and the like on Saturdays and close the park no problem at all.