Hi,
many thanks for the pictures as they do help.
The reason why your gpu doesn't pump air out of the case like the cpu fan because of it's design.
Graphic cards which push air out of the case are usually known as blower types of cards. The design you have ( like mine too) allows the hot air to simply spill into the case.
It looks like your cpu fan is the only fan extracting all that heat.
What you could do is fit a couple of 120mm or 140mm fans pulling clean air in at the front.
To better extract the heat you could try attaching 120mm or 140mm fan to the top underside of the case.
Here's a photo of the machine I built, notice how i have fans pulling air in at the front and fans blowing it back out at the top:
Update: I saw a tutorial where the person turned the gpu clock to -200. That's a bit too low I think so I turned it to -20 but so far it hasn't crashed. I'll play for +- an hour. If it hasn't crashed maybe that could've solved it?
Yup this is another way of dropping the temps or stress your card is recieving and won't harm the card at all.
So what you could do is use the card like that until you can attach some fans. I'll certainly help with any advice should you need it.
Glad to hear you at least found a solution of sorts.