@PeterFigen: I know, they shouldn't be edited. Datacolor already exchanged the device, same results. We have problems on several different monitor brands. I feel, Datacolor's calibration doesn't do a good job. Thanks for suggesting ProfileMaker5's Edit Module, I'll try that out.
@Glenn_UK: Thanks for confirming that Photoshop has no such capabilities. And I admit, I didn't quite understand the article I was linking to. I just read "Open Photoshop ... Save as a copy, and create a new icc profile with this file" So I thought, maybe Photoshop has a function I'm not aware of. The problem I experience is that the monitor - after calibration - has a slight green cast (when compared to an industrial greyscale chart). So basically, I wanted to bend the green gamma curve a bit down. I know, that this is not a solution, but I have to get a job done and need this as a temporary fix in the meanwhile ... better than nothing. I will study other calibration devices afterwards, I just don't have the time right now for this work unfortunately.
@GustavoSanchez+Glenn: Thanks for suggesting BasICColor Display4. I'll look into that.
@Freeagtent: I work on an Eizo Flexscan Monitor. It has several predefined working modes: Text, Picture, Movie, Custom, sRGB. Obviously exluding the first three, I settled for sRGB, because in this mode I can only adjust the backlight, nothing else and I thought - or at least hoped - that it would be closest to my calibration target (sRGB) and thus make me achieve the best calibration results (because the less the display output has to be "corrected"/"adjusted", the better). Also, in custom mode, I have several settings and therefore more possibilities to do something "wrong" ... so I thought I stick to sRGB, because there are no parameters and the SpyderCalibration has no parameters in that case either, so at least there's no possiblity for a user-error.
And thanks for thinking about it, but yes, my monitor is warmed up >1 hour and I have the ambient light detection set to off (as suggested by Datacolor's support). I have filed a ticket with them more than 1 month ago and every once in a while I get messages, saying they are sorry, they are still evaluating the problem on it on different systems/monitors, so judging from that, I guess they might have a production problem.