Acoustics

Are you using full-range or subwoofer(s). In any case, try moving to a new position. If I move my subwoof a foot to the right, the sound is unbearable.

As dweller suggests move your speakers about - the spikes you are experiencing suggest to me that they are the result of room nodes which can be changed by speaker relocation. Another possibility is to use a sub woofer crossed over at 120hz +/- and locate the sub in a different plane than the main speakers. I did this with some planers which were set up traditionally (triangulated) 5ft out into the room with a huge spike - put the sub against the wall between the speakers and ended up with an almost flat FR. (I'm not suggesting that that is a universal cure - but what is possible. A speaker manufacturer who posts here on occasion uses multiple subs to great effect. 

No sub. I've tried to change speaker positions over and over again. Therefore I bought a XTZ Room Analyzer and it is from those measurements I've got the figures.
I don't have room for multiple subs and I tried with one sub once, but it only got worse.

You might consider changing your listening position - too close to a wall for example can really boost the bass. Inches can make a difference. If you haven't already done so, you might check out the Cardas set up - it is at worst a good starting point for system set up.