Well, calculation is cheap. Where one exponential function won't kill the server, four won't either
I must reiterate that I have no idea about where the specific problems of Poker lie. Our ladder actually seems to have the opposite problem: Top players only playing against low-ranked players.
So concerning your mini-season (I would actually call it tournament at that scale): I quite like the idea of aggregating a score out of these. You could associate it with some Poker-related metaphor like a bracelet or something. Have themed tournaments, maybe with special rules or more worthwhile "prices".
But on the other hand, ELO isn't really made for such sort "spurts". Real tournaments work as well as they do (or don't?) because they have strict control over which player plays against which. ELO and friends just have to deal with whatever you throw at it. Players can then always abuse the system by constructing cases where the system doesn't have enough information to properly judge the situation.
To give concrete examples:
a) Say all players start with 1000 points, no "newbie protection". Now new players are most likely overrated. So players looking for a top score will to try to play against as many new players as possible. Frustrating new players in the process that most likely won't understand why they are preyed upon.
b) On the other hand, starting at 0 points, with "newbie protection" you might get a bias towards group that play a lot amongst themselves, because every time someone falls under the "newbie limit", everyone gets a bit of a boost. Might be hard for new players to get into matches with good players, even though they can at least earn good points by playing with similar-ranked players.
ELO is still a lot better than most simple systems in these cases, mind you, but there will always be problems. It might take a bit of tuning to get things right (Personally I'd favor start with 0, protection until 100).
Plus: The shorter the seasons, the more aggressive the style of play will be. With the infamous instant Pre-Flop-All-In being at the lowest end (= one-game-tournaments). Also something to consider.
These are my thoughts. Have fun