Ok I ran a quick and dirty mock-up just to confirm what lack of airflow can/will do.
I used my test bed, so keep in mind that it's an open case. Both this case and yours have external fans directed at the heatsink, but the AC 7 Pro probably gets more benefit from the fan because the fins run all the way through and in the direction of the external fan airflow. Your temp difference will probably be higher due to the fact that the external fan is only affecting the fins it blows directly on.
All I did to simulate the conditions in your case with the heatsink mounted that way was to use a piece of cardboard to restrict airflow on the "exhaust" side of the heatsink. I'm not convinced that metal would make any difference, but if it did, it might actually help in wicking away some heat where the cardboard would retain it. (acts like a giant heatsink itself).
This is a pic from the side (top of carboard was pushed closer during testing). You can see that there is at least 1" of space between the heatsink and the cardboard restriction. It looks like yours is closer than that, so I'd expect much more dramatic results from the restriction on your setup.
Ok, here's the results after 10 minutes (you can see when the restriction was inserted). Even when the cards are stacked to keep the temps down (better style of fins for using the large external fan, restriction further away allowing better airflow, and open case allowing better general overall airflow) there is still an immediate 3+ C difference in temp which would probably continue to increase over a longer testing period, under conditions more closely matched to yours.
If I had to hazard an educated guess... it'd be at least a 5+ C difference to your system with that kind of restriction, and I'd guess it'd be a lot closer to 10 C than 5.
__________________
EVGA X58 3X SLI / i7 980X / 3X 4G Mushkin Blackline Frostbite / XFX Pro 1000W / EVGA GTX 680 SC+ 2GB / Corsair F120 / WD 6401AALS / TT Lvl 10 GT
Swiftech MCP655 WC Pump / EK XT 240 Rad / 2X Scythe Ultra Kaze / EK Supreme HF / Primochill Myriad Dual Bay Res / Dell UltraSharp U2412M
Sabertooth 990FX / PhII X4 965 / 2X4G Corsair XMS3 / EVGA GTX580 + EK Block / Corsair 120G Force GT
Corsair TX750 / XSPC EX240 / Swiftech MCP655-B / XSPC Dual Bay Res / ? CPU block / Bitfenix Ghost / Samsung 931BF