In July 2021 we did that loop of lakes. We came down from Lunetta to Hassel and went clockwise to Boulder, spent the night there, and then went back to Phantom -> Battle -> Hassel -> Saca -> Crab -> exit. Despite it being high season, and with the closure of the entire western half of the park due to Quetico fires forcing us and others into the region south of the Echo Trail, the only occupied site we saw outside of Crab was the one on Clark, and the only other group we ran into was on the Crab-Clark portage. So you'll probably find solitude there, at the very least.
Battle seemed like a very nice lake. We saw a family of otters at the north end of it on our way out to Hassel, and spent a while waiting and watching them and taking pictures.
Boulder was isolated, and you can see some pictures of it in a recent
NTL. I was really looking forward to a swim that day after 1200 rods of portaging, but it turns out that Boulder has the darkest water I've ever seen in a BWCA lake, and it's mucky and shallow, so I had to go without.
Meat was interesting because of the low water level on the east side of the campsite. I didn't like the look of Hassel very much, it was surrounded by flat land and strangely rocky shores. The only lake we didn't do in that area was Glimmer.
If I were doing it again, I think I'd still go all the way around the loop, and still go out to Boulder just to see it, but Battle was the best of the lakes. If you come down from Crab, the Crab-Clark portage is the steepest I can remember in that part of the park. On both ends there is a significant climb right near the water. There is also a burn scar across the portage, which might leave you dodging blowdowns if you have a storm (that's what happened to us).