I was thinking that if the only 'weakness' (as to many it may be a strength!) of the K701/K702/Q701 is the slightly subdued bass perhaps a quick bump to those frequencies via an equaliser might create a better sound. But after doing more reading it appears that this is borderline heresy as would disrupt the balance of the headphone. But you're bang-on with your summation, as I've not tried anything before it's probably safest to err on the side of 'fun' for now, and perhaps move into something more specialised (be it sound stage, bass/mid/treble emphasis etc) once I've actually discovered my preference!
I read an excellent review here comparing the K612 against the K702. It appeared to be exactly as you described - the signature AKG 7-series sound but with a touch more bass and, if anything, an even better sound stage for gaming. At the current price (~£100) it seems almost too good to be true. Since then I've discovered that the current batch is made in China, and sadly from inferior parts to the model used in that comparison (which was made in Austria). And that worried me a little.
Strangely enough I've just ordered a pair of E10S in-ear headphones! Didn't realise they made bigger ones, so will give these a look. It seems they retail for around the same as the X2 though - are they in that league?
Do you mind me asking where you got the K612 from? I'm super-interested in your experience as I'm in a very similar position as yourself and have narrowed my choice down to either the K612, Fidelio X2 or possibly the HP200. Seems like the X2 is the more well-rounded set, however it's literally twice the price of the K612! And I think Stillhart made a very good point about the chances of the X2 dropping in price being relatively slim.