Yes, it's fine to post this info/request.

July 21/22 are great dates to get walk-ins, since they are Monday/Tuesday. So just go and plan on getting the walk-ins.

As far as joining a group, it gets a bit tricky, as you would be expected to camp together, and that's likely when the ranger would be checking.

BRH, in the three weeks before your trip, check online several times a day for cancellations. A few good people will release their permits there, and so you might be able to pick up reservations that way. Looking online just now, there are 4 and 2 available in the next 2 weeks window.

Bookmark this link, and start watching: Overnight July 14-27

In the meantime, if anyone has 4 open slots....