A few hundred dollars later, my ongoing attempt to have my second monitor cloned onto my video projector is still made of fail. What am I doing wrong here?

My plan was this:

2008 iMac mini-DVI-D output
→ Mini-DVI-D-to-DVI-D-female
→ DVI-D-male-to-2x-DVI-D-female splitter
1→ DVI LCD monitor (1600×1200).
2→ 30' DVI-D-male-to-HDMI cable
→ HDMI-to-component converter
→ HD15M-to-3xRCA cable
→ Projector (component input).

My plan fails in two ways:

1. If I just do this:
   iMac
   → Mini-DVI-D-to-DVI-D-female
   → DVI-D-male-to-2x-DVI-D-female splitter
   1→ DVI monitor.
   2→ (second output of splittter unconnected)

   then the monitor just sits there and flickers, trying to display a message about input being out of range. So clearly that splitter confuses the hell out of either the Mac or the monitor. I don't know which.

2. And if I just do the second part:

   iMac
   → Mini-DVI-D-to-DVI-D-female
   → 30' DVI-D-male-to-HDMI cable
   → HDMI-to-component converter
   → HD15M-to-3xRCA cable
   → Projector.

   I again get no signal on the projector. Sometimes I saw the projector displaying snow-crash; sometimes it appeared to be trying to lock on to various resolutions that were changing every 5 seconds; briefly, I saw something that appeared to contain the right colors in the static; and now it's decided to just always be black. Anyway, no worky. I tried all permutations of the various switches on the device, and all permutations of the 3 RCA cables.

Suggestions?

Update, 2011:

Here's what I'm using now, and it works:

iMac
→ Mini-DisplayPort-to-VGA-female (or whatever), $30.
→ Atlona AT-VGA300CV Converter Scaler, $300.
1→ VGA monitor (1600×1200).
2→ component video (1600×1200 scaled to 1920×1080) to projector.

Previously I had been using an "Audio Authority 1366 HD Scaler" instead of the Atlona AT-VGA300CV, and that worked fine for three years, but then it unceremoniously croaked. All evidence suggests that the Atlona has exactly the same hardware inside, but is $30 cheaper.

A full scaler is necessary because my projector will not accept a 1600×1200 signal encoded as component video. It has a small set of standard video resolutions that it can cope with on component (e.g., 480i, 720p, 1080p).

I haven't found a solution that gives me a digital (DVI) pass-through from the Mac to the monitor, but with a good, short VGA cable, it looks fine anyway.