I have to say that I too have been thoroughly satisfied by Hilton’s prompt, generally accurate resolution of issues I’ve addressed by email. I’ve been a Diamond member for almost 6 years now, and once or twice a year I have to email about a stay that didn’t post, or points for a second room that didn’t post. Just as you describe, I receive a confirmation email acknowledging my email, followed by a resolution within a few hours, rarely more than 24.
From experience, one thing I can say that will expedite a missing stay request is to scan a copy of your folio for the stay in question and attach it to your initial email communication with the Diamond Desk. This almost always results in a successful resolution on the first email. Interestingly, I haven't had to ask for points on a second room in over a year. It seems that the software Hilton is running has improved and is automatically posting points for a second room now without much additional intervention by the Diamond Desk.