I feel your pain. My club has done many "tiered" tourneys, and sometimes someone enters who is not supposed to do so. It is very annoying to not be able to remove them (or have them remove themselves).
As for everyone playing in the same tourneys, it is a problem, and worse, it's a problem that some people refuse to acknowledge. They state that WGT already levels everyone and why would we need to handicap things further.
However, for exactly one tournament a month, I did manage to get most of us together, which I did by inventing a proprietary leveling system.
Without revealing exactly how it works, it utilizes two different factors from the WGT leveling math, in addition to several factors from the country club play itself. By doing this, we are able to group folks into five relatively even groups (in our club), and people are being grouped by so many criteria that it's very hard to sandbag.
This way, someone can feel like they've "won" a group or done very well in it, even if they don't win overall. It's the best we can do, because as you point out, folks just won't play if they don't feel competitive.
Jay