Here is an idea of how to allow "drafting" decks in an environment where not many people are online at the same time. It's a mechanism inspired by the Hearthstone arena mechanic.
Upon joining a league, player is given an opportunity to "draft" cards for his league deck. The draft procedure is as follows:
1. Player is given a preset cards/packs (pack selection if needed), ie. 9 sites, ring-bearer/burglar, The One Ring for non-Hobbit formats, etc.
2. Player is presented A times (number TBD) with a choice of B cards (number TBD), and player can choose one of those cards to add to their pool.
3. The presented cards are randomly chosen from all cards, or alternatively - first a card tier is selected (for example by rarity, but this can also be configured by a configuration file, ie. by power level), then the cards to present are randomly selected from that tier.
4. (Optional) The tier selection for first few pick(S) can be forced, ie. show random cards from a pool of powerful cards, or cards that give a deck direction (ie. powerful minion that works well with other minions of this culture).
5. (Optional) We can alternate shadow/free people tiers to ensure that player ends up with a balanced card pool.
6. After player finishes the draft portion. They can build a deck for that league and then play games in it.