Jim,

But I have to say, because I think it’s part of the issue here, that when I hear phrases like “public, communal absolution and grace,” there is a part of my brain that lights up big letters W, T, and F. I have absolutely no idea what “communal absolution and grace” even are or why I would need or even want them [emphasis mine]

I can’t speak for you but I can tell you why I want them.  Deitrich Bonhoeffer said:
He who is alone with his sins is utterly alone. It may be that Christians, not withstanding corporate worship, common prayer, and all their fellowship in service, may still be left to their loneliness. The final breakthrough to fellowship does not occur because, though they have fellowship with one another as believers and as devout people, they do not have fellowship as the undevout, as sinners…

When I take communion with other believers, it’s a acknowledgement that we are all sinful, we are all utterly dependent on God’s goodness towards us, and that we are all in the same boat.  Ask an alcoholic about the power of an AA meeting.  It comes primarily from the shared experience of failure, the shared hope of redemption and, if not absolution, than at least forgiveness.