This is getting complicated fast
I was suggesting that you should try swapping the cards, not even as a defintire answer, but more as a confirmation that the PI has the room for a Type III card.
The two motherboards loke nearly identical on your pictures. I know that the Arima special fits in the 3438, it has been tried, so it shoúld fit in the Pi. I agree, though, heat may be an issue. Going from a x1400 to a 6800 woul most definetely be a nice performance increase, tho
Adding heatsinks in the inside is pointless as lonng as you can't evacuate the heat.
The problem seems to be a compatibility issue between Gateway MXM cards and FSC. That's why I would advise against buying the 7800 to replace the 6800 right now. I assume replacing the x1400 with the 7600 might give the same problem, even though the different Bios migh make a difference... I don't know.
But if that's something you'd wish to try, I'm willing to ship it to you, free of charge. I only ask you to return it to me if it doesn't work or to pay for it if you want to keep it.