Need Help Researching TV Output Via A Nvidia GTX 260

My Question
I used to use a program called TV Tool, before Nvidia drivers and Windows included solid official support for TV Output via graphics cards. It was very effective when the drivers and OS had failed me. That software was only useful with very specific TV chipsets though so it is of no help to me now.

I find myself in a similar situation and am trying to find software that is intended for controlling the output of a graphics card to a Television. Every time I search on Google for "multi-display", "multi-monitor", "graphics card output" or anything along those lines, all I find is information relating to using multiple monitors to display a single Windows desktop.

I'd like to be able to force my desktop to display on my TV as I am having trouble doing this reliably. I'm willing to do the research myself but worry I am using the incorrect terminology for what it is I am trying to search for. I have little experience troubleshooting problems with TV Output. I was hoping somebody could point me in the right direction or perhaps recommend some software they're aware of.

Any help would be greatly appreciated. If you'd like to know more about what is specifically going on, please continue reading. Thanks!

The Setup

1. I have a NVIDIA GTX 260 which has two DVI connectors for monitor usage.
2. The right DVI has a DVI to HDMI connector on it, a HDMI cable plugged into that, which is in turn connected to a TV.
3. The left DVI has a DVI monitor cable plugged into it, which is in turn plugged into a LCD monitor.

The Problem

1. When both the LCD monitor and TV are on, I am unable to use Windows 7 or my NVIDIA drivers to force the desktop to display on the TV. The TV often says "No Input Source". Going into the Windows Screen Resolution window (available from desktop context menu) and clicking on the Detect button will sometimes work, and sometimes won't.
2. If the HDMI cable is unplugged, the TV input for displaying the monitor is not available. The card must be plugged in for the TV to switch to that input.
3. If the LCD monitor is off and the TV is on (HDMI is plugged in), I have identical results as described in #1 above.
4. If I fiddle with turning the TV on and off, the monitor on and off, clicking on the Detect button multiple times, and/or try enabling and disabling the monitor - the TV - or both in the Nvidia drivers, the monitor will eventually appear on the TV. So I know it can work. When it works, it works flawlessly until the TV is turned off.
5. I have played with all manner of setting combinations between everything mentioned thus far, have researched each element, and have had zero luck getting this to work reliably.

My Suspicion
That the graphics card has trouble detecting my TV or vise versa. This is further supported by me hearing the Windows sound for hardware being added/removed, as I mess with various settings. It is most often heard when turning the TV on and off.