If you look at the manual you can see a 7870 is on the list of officially supported cards and they use a blower standard spec 7870 which is ~10inches. Also if you look at the manual you will see they add a stabilization back end to the card for shipping reasons which itself is 2-3 inches. So honestly he could even get a 980 in there pretty easy I just don't think the extra 250$ is worth it.
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That is definitely not an issue. See http://anandtech.com/show/7189/choosing-a-gaming-cpu-september-2013/8
That is a list of every cpu architecture for the past seven years or so. Sort of some magical super jump with skylake which I doubt is going to happen you are going to be fine. Notice the i7-950 that cpu is slower than yours clock for clock by a good amount and it is also a first generation i7 where as you have a third. Notice it is only 1 fps behind your cpu. For a more extreme example see the 920? that is 2.66-3ghz to your 3.3 to 3.9 with only 6 more fps in your favor.
And that is just comparing ghz not even accounting for the fact that the your 3770 is about 10-20% more powerful clock for clock depending on the task. So in reality if you want to equalize that then its ~3.6ghz - 4.29ghz on the low end compared to 2.66ghz - 3.00ghz and that only yields ~6 fps.
So your cpu is fine for some time to come. The psu definitely needs upgrading however if you want to venture into better gpus.