We have a usergroup who do not act upon reports, but would like to have visibility into reports should the need arise. I may have missed it, but I can't seem to find an explicit toggle for allowing moderator control panel access, or even to just the report center. Does such a setting exist?

If not, how else might one grant access to the report center without any of the functionality typically granted to moderators? Could I do this by basically turning off everything for that group under ACP > Staff > Moderators?

Yes, create a new moderator (group or user) and enable only Can view reports? permission. Disable all others