Well, as has been said to death, you need to close that case up. If even after closing the side panel, you need to consider a different case entirely. A Fractal Design R5 or similar case with a front panel door and case dampening, and possibly exhaust baffling is what you need if you are still having noise issues. The other option is a passive cooled video card but that means stepping it down quite a bit in performance.
I have had a HD 5970 in a Fractal Design R4 for a bit, but it was even able to tame that beast (for reference that card was as loud as a SLI 680 GTX setup... and a single 680 GTX being aprox 6 db louder than a 1080 Ti, it would put it around 14-16 db louder than your 1070). A good case is able to dampen the noise levels. I havn't seen a better case for relatively cheap cost as a R5 do a better job at cutting the noise.
Just as a footnote, I've been able to more effectively muffle fans by building two or three layers of Spire foam-rubber circles with diameter of the fan hub, and sticking them on the fixed part of the hub. On the ubiquitous 120mm or 140mm rear case exhaust port, you can simply stick a "barrel-nose" of this type over the case in line with the fan hub.
But that trick won't help with the graphics card's proprietary fans. Off the top of my head, I can imagine building some layers of Spire foam to stick on the plastic shroud of the graphics card to surround the fan, but you then have the problem of removing the Spire as you might wish. The depth of the Spire layers would only be limited by the proximity of any other PCIE cards next to the graphics card. Of course, the Spire foam-rubber is non-conductive for any such considerations of adjacent PCIE cards.
Also -- this. I've now taken a closer look at the Cougar case. There are vents on the case side-panel for fans there. You could perhaps ADD a 140mm fan -- mounted to the side-panel to isolate contact with it, and with a quick-disconnect of the wiring to the motherboard. If that fan would clear the graphics card, it would provide more ventilation to it.
I would also pressurize the case by using the front-panel AND top-panel fan vents for INTAKE fans. Block off unused vents: foam art-board from Michael's Arts & Crafts is good for this, and you can get the art-board in charcoal-black. Otherwise, for case-sidepanel vents that are unused, get a piece of Lexan from Home Depot and secure it to the unused vent through the holes and mounted on the inside of the case panel.
For 120 and 140mm fans, someone could offer more alternatives, but I'll submit these: Akasa Viper (either the "round" model or the square design), Bitfenix Spectre Pro LED, Noctua (iPPC is my usual choice). It would be very helpful if all the case fans, exhaust and CPU fans are PWM and controlled from a splitter (
Swiftech 8W-PWM for instance), or multiple splitters as determined by the available mobo fan ports. Then you would have motherboard thermal fan control by groups of fans. ASUS boards provide fan-ports that allow for either voltage 3-pin thermal control or PWM thermal control.
If you can, provide intake fan filtering with parts from
DEMCiFlex . If you need to use it with the DEMCiFlex filters, get a $4 roll of magnetic tape from Home Depot. But the Cougar is steel, and the only place you'd need magnetic tape seems to be the ventilated side-panel window.