Different options and opinions are definitely welcome, so thank you. I'm not also sure whether I understood all aspects of your proposition (for instance, where are tie-breaks needed for - to establish which teams possess higher "team strength rating"?), but that doesn't mean I couldn't reply to a message. ;)
What do you mean by SUMO? (I know only sumo wrestling, and as far as I know, not everyone meets everyone during one tournament, and it could be years that some wrestlers don't face each other as there are about 40 wrestlers on the highest level and 15 matches per tournament - and in some occassions they never meet unless it's mandatory to decide a tournament winner. There are rankings that change after each tournament though, so that's why I wonder if you meant that).
At the first thought I'm supporting your idea that weakest would face weakest and strongest face the strongest at the end of the regular season, however, as of now I think it'd better and (for the league commissioner probably easier) to use salaries in some form to determine the weakest and strongest teams. Also, if I'd personally have to create schedules (of which I have no experience of), I don't know how much more complicated that would make it if there are plenty of participants.
Also, I think it might be more transparent, more clear (and some might feel, more fair - however, I realize salaries might not the best way to determine the value of the players, but it's probably the best one that's viewable to all and therefore can be verified by anyone) to stick with some values that are more easily comparable and in one sense, more logical. I guess salary would also reflect better the real strength of the team in the given/following season (as opposed to last seasons regular season success), so using salaries as a base for determining such things would create more even groups.
I think it'd be great to also consider establishing rating systems that wouldn't require that much work to be determined (ratings made by calculating and comparing salaries unfortunately are not automatic either if you do it manually, so someone would have to overtake this job once per season), and that would be transparent enough (if such ratings would be used that demars suggested, who would create those rankings, on which basis would those be made, and would the rankings sort of be valid anymore for the season 2 that they're being used, if some homegrown team decides to sell player(s) close at the end of the season 1 for instance while still maintaining high league position at the season 1 league table), unless of course those "team strength ratings" would automatically be determined only by the regular season table. Also, if new teams join for the next season, sticking with salary would make it easier to put them into a "correct" group based on the team strenght (if there even would be multiple groups in the league), as a joining team wouldn't have any ranking (if ranking is understood here the way manager demars wrote about it) based on last season play, as they weren't participating in the league.
Having said that, while it all might have sounded negative and like I'd try to shoot down your idea, that's not the case. Things are not black and white, and there's good in every option (some more than in others - but that's how things eventually get decided, by comparing pros, cons and preferences). I was simply throwing out some thoughts that it awoke and trying to give some insights why I think this way currently.. As of right now, because of many reasons, personally I'm still fan of using salaries to compare teams strength ratings (so far I haven't come up with a better option, if I will, I'll change my opinion).