Aside from Zambezi being barely passable (sad, because I love the brand - they've just been mismanaged to near-death), one thing I would like to remind you is that you just switched from AMD/AMD to AMD/NVIDIA. AMD tests their drivers very thoroughly to ensure their compatibility with each other (GPU<--->Chipset<--->CPU mainly) and NVIDIA/Intel is much the same way. You do NOT however get any cross-compatibility from either side because neither is in the business of promoting the purchase of equipment from the other side.
In fact, it is quite the opposite - with DirectX 12, you can put together say an R9 Fury with a GTX 980 Ti (with the AMD in Primary PCI express slot, and the NVIDIA in the secondary - for some reason it performs better with the AMD in the lead, which is likely due to the architecture emphasis each company has, but that's also very much beside the point) HOWEVER neither AMD nor NVIDIA has been willing to provide support to help stabilize this, it has to come from each individual title's manufacturer which means this cross-compatibility is likely dead in the water.
All that aside, yes it would be a good idea to take apart and thoroughly clean your rig, and then to relocate it onto your desk top if you can (depending on how you have it set up, you can likely put it behind your monitor(s) crosswise so that you can access the ports and buttons by reaching to either side of your video setup. It would cost you nothing but the game downtime to test this out.
Into low-cost options, you could consider reselling your 970 and getting an R9 series (if going that route, I would limp along with your old GPU until the new HBM2 cards are released and the prices for the current cards gets pushed down to stretch out those pounds). You can also replace your case fans as they are cheap and they could almost certainly could use it.
Into somewhat higher-cost options, you can update your main board/cpu and go Intel. That is purely your choice and you should not listen to anyone saying what is "better than the other" but you really do want to keep your CPU/GPU/Chipset as matched as possible so your drivers will have less conflicts. You can get a decent main board and processor set at just about any price range, so you would want to do some research to see what best fits your options here. Be careful to review your chassis specifications so you don't force yourself to buy a new one if you go this route, unless you want the costs to start jumping significantly.
Another thought, and this is a low-cost one again - if you have some tools and a little ingenuity, you can modify your case to allow you to mount it higher in that tower cubby. You have no perforations at the top, so you could run bolts through the top of the case through the desktop. Personally, I would use pinned posts like race cars have for holding their hood in place, so that you can support the case from below and pull the pin to remove from the desk quickly. This will get your underside openings into open air that isn't so close to the carpet. You could also cut/remove the cubby from of the desk and allow a completely open-air installation, and you could mount the tower anywhere on the desk you like - just make sure that it won't interfere with your peripherals.