Hi Fabrice, welcome onboard! I'd like to make three requests, if I may.
1) Like Brandon said in the "Gaming the system" thread - go with the qualitative feedback option. In terms of recruiting new editors, giving people an easy way to give constructive feedback in words (not just star-ratings) will identify those potential new-editors who are happy and able to give good editorial advice can be engaged by the existing community to contribute directly. Currently, the star-rating system doesn't help us separate the more literate reviewers from the people who just like clicking things. Furthermore, giving feedback in words is actually useful for the existing editing community. Currently the tool is only (potentially) useful as a recruitment device for new users and the actual reviews that are given are not being used by the community which is only driving resentment to the tool "cluttering" the space.
2) I've said for a while that the quantitative reviews (the rating scales) will only really become useful when they are expressed over time. Show a 4-coloured line graph (for each of the criteria) over time and then editors can quickly see if the article is improving, declining or if there's an unexplained spike that could imply someone trying to game the system. As it stands, having a single number (even if the older reviews "expire") does not tell us anything that the talkpage assessments don't already do - and more often that not they don't even do that.
3) Hide it from logged-in users :-) A large proportion of the people complaining about it are asking for aesthetic improvements so it does not take up so much room, or at least be centered. Since the tool is only asking for reviews from the readers (not editors) why not just auto-hide it for logged-in users. The qualitative and/or quantitative feedback it generates can be made visible somewhere else (e.g. on the talkpage alongside the article's quality "class" and "importance" assessments).