That's a tough situation all right. In the end, it can probably only be solved if all owners step back and take a look at the best interests of the league as a whole rather than their own teams.
If this sort of trading is threatening to destroy your league, you might have to ban the trading of draft picks entirely. Teams would still be able to trade vets for prospects, but there would be less room for abuse. That should probably be only a last resort measure, however.
The best way to solve this might be for those teams that feel they're getting left out of such trades to talk more with the teams that are making these deals. It's possible, after all, that these trades aren't the result of favoritism, but that the people involved merely spend more time talking. Having previously received fair deals might also be a factor. If I'm looking to make a trade, I'll probably also start by knocking on those doors where I've been treated fairly in the past. If the teams that object to these trades spend some time on the phones (or email, or whatever) and offer solid deals, the problem might go away by itself.
The rules you've tried so far actually look pretty good to me. I don't really like the idea of posting a trade and letting other teams make higher offers - if you've spent a week working on a deal, you'll probably feel pretty upset if you're outbid - but putting constraints such as an early deadline on draft picks or a limit on high picks that can be dealt sounds like a good foundation.
Another thing to try, if this issue can't be resolved through good will alone, would be to assign each team one other team that they may not trade with, period. If favoritism truly is involved, then simply take away that possibility; if teams A and B are brothers, for instance, decide that they may not trade with each other any longer in the interest of the league, at least until it's been shown that other trade avenues are being used equally. An even number of teams would help here, of course, so that every team would have just one other team they may not deal with. This isn't a wonderful solution, of course, but if the other measures you've tried have failed, you may have to try this.
What are the specifics of your league? Do players have salaries? And do teams have the right to protest or veto trades?