My frustration is how it always seems like my opponent drains his ball just BEFORE the ball save times out...but my ball drains just AFTER the save times out.

Yes, I really prefer the limited qualifying. It seems a lot more fair than "the guys with the most qualifying attempts get to qualify".

I'd prefer a sort of hybrid thing, where everyone gets 2 or 3 qualifying chances.

I understand that it sucks to not qualify just because you had a "bad round", but if you've had 2 or 3 "bad rounds", then you probably shouldn't qualify.

The "pump and dump" thing is bad for three reasons.
1) some players can just "buy" their way in by spending the whole day(s) doing qualifying attempts.
2) even if you do well, your score may not hold up against all the "buyers", meaning that you need to keep doing more qualifying "just in case".
3) because of (1) and (2) the lines to qualify get longer and longer until you spend all your time either qualifying or waiting to qualify.

The main reason tournaments do the "pump and dump" is because if you charge the players for each qualify attempt, you can rake in a bunch of cash.
It's not a good way to run a tournament, but it IS a profitable one.

Yes, the quality of players at small local tourneys will vary wildly.

I was in Tampa on business last month, and saw that a local arcade was running their Thursday night tournament, so I decided to try it out.
I wasn't really expecting a bunch of serious players.

It turns out their tourney is "always won" by Eric Stone (who just won the IFPA World Championship last weekend).

So, you just never know...(and congrats to Eric Stone on his big win!)