Your "seed" is determined by your rating. In any tournament that is not "random seed", you are going to have one of the top seeds and you are going to be making a table. No matter how we might alter the number of top-rated players at a table (which is your particular beef here), you will be the highest-rated of the ones at your table, and so you will be setting.
As to byes, the system is set up (as all rating systems are) to give byes to the top-seeded players in a given tourney. That is not going to change, it is fundamental.
The solution is already to hand: "random seed" tournaments. If the TDs hosted more of these (assuming they are not regularly used already) then you'd have plenty of tourneys that were specifically tailored to your desires here.
Ain't life grand? Just, all of you who want these, ask yer admins very nicely, "Please, may we have more random seed tourneys?" If enough want them, or if they become wildly popular, I'm sure you'll see a lot of them.
What's interesting here is, it's rare to see a very high-ranked player asking for random seeds, most of them are happy with (and feel they've earned) the bye.