On balance I would probably agree with you that Becker had the greater career. There are a few things in Edberg's favor besides the fact that, as you rightly say, his game was obviously aesthetically more pleasing. (By the way, Edberg is not just my favorite tennis player but my favorite sportsman or sportswoman ever, so I know a lot about his career).
1) Edberg had a better career record than Becker at all of the Slams apart from Wimbledon. (Yes, it was better at the Australian Open. By a lot, in fact).
2) Edberg won four of their five most important matches (the fifth most important being the Masters final of 1989).
3) Edberg finished as world #1 twice, and Becker never finished as #1. I know that Becker had a case in 1989 and that Edberg's case in 1990 wasn't unquestionable (and that even in 1991 he was only a narrow #1). I know that you don't count rankings in your system, and I can understand why, but the fact is that many people do think that rankings matter and they probably weight that in their calculations.
4) Relatedly, Edberg ranked higher than Becker in all of 1990, 1991, 1992, and 1993. Moreover, although Becker did rank higher in both 1988 and 1989, I think most view Edberg as having had a better season in 1988. Bearing in mind that Edberg also ranked higher in 1987, I think that that means that many would think that Edberg was better than Becker in six out of seven years in the heart of their careers (1987, 1988, 1990, 1991, 1992, 1993). I think that this points to an important reason as to why *some* people think that Edberg had a better career, or at least think that it's closer than you allow: Becker had a horrible mid-career slump, while Edberg did not. Although Becker did much better later on in their careers (from 1994 onwards) and slightly better early in their careers, he wasn't the best player in the world, and was clearly not the best player in the world, in either period. Thus, there was a substantially longer period of time during which Edberg was at least roughly as good as anyone else than there was with Becker. I think this leads to a widespread perception of Becker as a talented underachiever who never made the most of his early promise. I believe that you think achievements should be quantified to purify us of those misperceptions, but I am here trying to explain what the perceptions are. As I said, I would agree with you overall, but not by as much as you say.
On another note, I have read your system of quantification and do have some thoughts on it. I will say that I think it's a pretty good system. I do think that there are arguments that can made about the things that you include and the things that you don't, however. If you would like to discuss it, I am happy to give you my thoughts, but please give me a few days first!