I was actually on La Muir yesterday and checked out a few sites I had been curious about. The best site IMO is still on the north shore. Middle one in the group of 3.

I would say it is better than the western island beach site on Hogan ( eastern site) only because if someone takes the nearby site you can hear every word they say. Never stayed on the western island site, just because so many people rave about the eastern beach site.

When I stayed on Hogan two years ago I stayed on the Eastern site on the island.  It's a good site.  You can hike the ridge on the island to the other site.  There's a large raspberry patch when you get close to the Western site.  You'll probably be too late for that in September.  While I was there there was someone staying on the "point" site in the middle of the lake, and I could hear them quite clearly despite the ~1km in distance.  The other site on the island wasn't as good as the Eastern site in my opinion.  The site on the shore near the island has a weedy shore.  The "point" site didn't seem too appealing, and the other site around the corner......I've passed it twice and I don't really remember seeing it.  Probably not good.

From Hogan I passed through la Muir, and the only thing I remember was the site closest to the Hogan portage was taken.  I think it might have had a beach.

I passed through Hogan heading to Philips just a few weeks ago.  The Western most site in Parks Bay looked interesting, with beach potential.  The Western-most site is a huge slab of rock heading into the water.  Also has potential.  If you're not coming from Philips these might be more out of the way if you're heading to la Muir next.