Q's about Recording PC Gameplay for Streaming (2 computers)

[pvraag]

Purpose: Stream my PC Gaming to a streaming service like JTV

I've usually done this with screen capture software (VHScreencap) and encoder (Flash Media Encoder), which works to some extent but comes with several problems.
A) Not every game allows full screen capture for whatever reason so I'm forced to play windowed which is not nice.
B) Performance. FME is quite the resource hog and even on my multicores simply makes it a constant juggling act that makes playing some of the newest games not worth it.

So I've been trying to think of other solutions for this.
First, available Hardware:

PC1: AMD Phenom II X6 1055T with HD5870, Asrock 870 Extreme3
PC2: AMD Phenom II X3 720 Black with HD4870, Asus M4A78 PRO

Dazzle DVC 107 video recorder
Black Magic Intensity Pro (BMI Pro)

1) I have tried using the Blackmagic, using an HDMI cable from my main computer to the BMI in the second computer, clone the monitor. This *may* work, but I have yet to find a configuration that allows my BMI to capture the screen so I've had no luck so far.
2) I think I read about someone using the Dazzle as a capturing device for TF2 at one point but he happened to have a Video card with an S-video out, which my cards sadly don't have any more.
I was thinking maybe a cheaper second video card in my main computer might be an option but I don't know if that could work. It would have to allow my main graphics card to do the work, and allow my secondary graphics card to simply clone the screen.Q: Is that even possible or does it need to be an equally strong graphics card?
3) For Audio I was planning to use a simple cable to go from my audio out on one computer to the audio in on the other (Synch problem?). Not sure if that works well. If anyone can think of a method to introduce or reduce any form of delay in audio, either hardware or software that would be nice.

Any and all suggestions appreciated since I would really like to get this to work.

Ideal Solution: Play my games on one computer, Record and Stream them on the other.