I must be missing something, but I don't really understand what exactly you' trying to achieve. Will you save anything by replacing your cable box with your PC cablecard tuner?
I use
Philips Digital Satellite Splitter SDW5012o/17 to split my cable TV signal. I pay for one TV only and watch my cable TV on my 3 TVs and on a PC using a TV Tuner. I don't need my PC to be turned on to watch my cable TV (besides I don't need to rely on Windows and Windows Media Center). I'm absolutely satisfied with the quality the splitter provides.
I do record TV programs using a PC TV Tuner. I do prefer to use a mouse and to change recording settings for every program. While I do believe many people prefer to use a remote control to record TV shows.
If you want to save some money, you can watch over-the-air (OTA) TV.
TViX R-2210 is a good way to replace your cable DVR. It allows to record HD programs the same way a cable DVR does.
Your computer is very powerful. As you are not going to connect your PC to TV or monitor directly, but just use it as a streaming server, I suggest you to try to stream content without any expensive graphics cards. Some graphics card do allow to decode video without using your CPU, but I'm not sure whether this functionality can be used when streaming content to a network.
Hope this was helpful.