Holy SCHMAKS! haha. That is one awesome setup! Well I can certainly tell you that with 2 xeon cpus, and 5 video cards I'm not surprised that your system is running so hot. Jacob from EVGA said that the backplates actually improve the cooling on the video card, so removing them "might" not help. The removable parts, were part of the design to help allow airflow into the blower fan when multiple cards are stacked together, which is why your cooling got better after removing those, so I don't know if removing all of that would help, as the 980 mosfets and memory are getting added cooling from the thermal pads on the backplate thats there. I personally would look at increasing the air flow, and lessening the flow resistance in your case, to help lower those temperatures before I removed the backplates completely. Here are my answers to your questions and the the things I would suggest, if my two cents are worth anything:
 
1. Removing the backplate does NOT void the warranty. In fact, neither does removing the cooler :) When you buy a new backplate from EVGA, there are included instructions with extra screws/hardware to remove the current plate and add the new one. So they have you covered on that. Buying an evga backplate, might not be a bad idea. 
 
2. Adding new fans in your case would be a great idea. Out take fans at the top would be a plus (while making sure that the fans on the cpu cooler are blowing the hot air UP and not DOWN). I would also suggest replacing that front middle fan (the one in front of your hard drives) with a Static Pressure fan to help move the air past the harddrives, or remove the cages and try to relocate the harddrives somewhere else to help more air come in the front of the case, and then the front of the blower fans on the 980s.
 
3. I would make sure that the outtake fan on the back stays an outtake fan. I don't imagine that cool air coming in from the top is going to help the video cards much when they're at the bottom. Getting a bigger case to allow for better cable management and higher air flow will be more effective. That mess of cables in front of those cards will definitely impede a steady air flow of fresh air. 


Honestly, even after all of this, your cards are still going to run hotter than most because of how much hot hardware you have packed SO CLOSE together. Liquid cooling the cpus might help take some of the ambient temperature, though I don't think that would be my first, second, or third option since it would be so much work and cost a lot. But definitely get more air flow going, with LESS cables in the way. Zip ties and cable clips will help at least minimize their footprint.

If you are going to have cards that close you need to mount at least 3 very high rpm fans right on the intakes of the reference cards or on the side. My 3 way setup would run in the high 80s. After mounting 2 3000 rpm fans 1cm away from the GPUs, my temps dropped from 88c to low 60s under 90% load.
If you can bare through the video a bit you will see how I mounted the fans and it was night and day difference. 
http://m.youtube.com/watch?v=l9FnEPo_ISg
 
Bottom line is you need to get a lot of air forced in between those cards.