In theory you could participate in this league under the same philosophy as the rumbles: compete one week and drop out the next. Extra cogs could be added whenever teams join.
However teams only get to play a single game/match each week, and unless you keep playing consistently it is basically a weekly random scrim. Which is cool, but probably (maybe?) not what people look for in a casual event. Because you can't win the event in a single weekend. You can just win a single game/match. Which is cool, but not really that exciting. People looking to enter into a single day, no-commit event want to have a conclusion.
I'm pretty confident that your 2 major problems could be solved creatively, and it would be exciting to have a variety of every-week-play Leagues to rotate through.
I guess my biggest worry is that these long events could stifle new things. I'm already concerned enough about the length of HC without wondering what will happen if there isn't a consistent opening for a 1 day event running on Sundays for people to play relaxed. Not to say it couldn't be done, or done successfully, just that it (IMO) might not return the benefit of trying to hold onto Sundays for having events that can conclude in a single day.
Here's a possible solution to the initial seeding problem that makes your initial position less important (possibly):
Every week you play a match. The result is you either win and advance (1), win and hold position (2), or lose (3).
(1) You are awarded with 95 points.
(2) You are awarded with [50 - (2 * Z)] where "Z" is your depth in the Cogs -> A team is Z=0, B teams are Z=1, C teams are Z=2, etc.
(3) You are awarded 0 points.
This results in advancing teams being awarded good points (but not enough points to switch between winning and losing repeatedly and beat out the top team holding "A" all season).
Teams that hold position are rewarded with some points.
Teams that lose are not rewarded.
Your starting position matters less because although you can earn more points for holding a higher position, you run a higher risk of losing and getting no reward.