Yup, the K612 is definitely a power-hungry headphone... But feed it well and it will reward you! On the E5 (btw they're supposed to go on sale tomorrow, so you might want to ask about a price match), you might prefer high-gain mode. The K612 used a higher volume setting than the 600 ohm Beyerdynamic DT880 for me!
The description of SBX you wrote, where increasing the surround just increases the echo, seems to describe a settings issue where SBX is only receiving two channels... This might feel like a weird description, but just go with me: BF3 & 4 have a "headphone" and a "home theater" mode, "headphone" mode processes a headphone surround "mix" and creates a 2-channel result BEFORE the audio gets to a soundcard and before SBX can process it... and SBX surround just adds a bunch of undesirable reverb to 2-channel audio. The settings you want: in the Windows system sound panel, you need to check the 5.1/7.1 channel setting. Then, in the BF game, you actually want to choose the "Home Theater" setting to get max audio quality with least processing. Finally, your E5 should actually be receiving a surround input now. I recommend turning off everything but Surround till you get the hang of it, and try 67-100% setting on surround. The processing won't work right if you didn't have the right three settings: Windows 5.1/7.1, BF4 "Home Theater," and SBX surround.
And you should avoid volume dials on headphone cables if at all possible, any reduction from max there just adds resistance and muddies the sound detail... Just leave the headphone at max and have your PC start from a very low %... It's at like 20% for me. On my K612, it's a bit higher, but safer for your ears to start low