I'm posting this from my Mac Mini, on OS 9. Ross, everything worked as planned. I didn't need to bring my CRT monitor along, afterall: picking up a VGA cable to plug directly on the monitor was all I needed. A DVI-to-VGA converter was used on the Mini's end.
(Note: At first I tried using the converter on the monitor/TV's end, combined with an analog-signal-capable DVI cable, but then the cable wouldn't have enough room to be plugged on it, due to the way it's physically constructed! That's why I had to switch the converter and cable around like I did.)
Also, as reported by others, no sound works at all, currently. Out of curiosity, I did try following DieHard's tip and partially plugged a pair of earphones, expecting sound to finally work, but no matter how much of it I plugged in or left unplugged, no sound came from either the Mini nor the earphones.
By the way, this LED monitor of mine really doesn't seem to be well-suited for anything other than HDMI, but, despite an odd "blur-to-the-right" shadow kinda thing, Mac OS 9 on the Mini is perfectly usable with it, visually. I'm currently using it at 1920x1080p 60Hz with Millions of colors pre-set, and it works just fine. The blur would be a bother for the eyes for daily use, so I think I'll dust off my CRT monitor anyway, but this is still pretty acceptable.
Again, I take my hat off to you guys' success on this. What an accomplishment, what a feat. With the respectful clock rate, and a driver-compatible GPU, it's as if the Mini was DESTINED to be mainly an OS 9 machine.
This runs so juicily!