So we want to have a draft Strat league...but we don't want it to take forever, and no one wants to have to do too much research. I've got an idea to fix that, based on how Magic booster drafts work.
Each person in the league will pick two MLB teams (we'll get to that procedure later). I'll remove all of the players with too few at-bats or innings pitched, so each person will have a stack of around 40 cards. Everyone looks through their stack, drafts one player, and then passes their stack to the left. Rinse and repeat until everyone has 26 players and a home park (yes, we're drafting those too).
Why this way? First, the draft will be ludicrously faster, since everyone picks simultaneously; if we all stick to 5 minute rounds, the draft will last less than two hours. Second, you only need to think about the few good players in the stack in front of you rather than every player in the draft, and that means less advance research.
Other details: I'm leaning towards a version of Brian's "relaxed schedule" idea. Play whoever you want each week, but by the end of the league you'll have to have played a minimum number of games against each other team (so you can't just keep beating on the weakest link). Injury lengths are capped at one series. We'll use the solitaire rules for player availability (each game, three position players have to roll versus their real-life at-bat total to see if they can play). We can probably go with most of the super-advanced rules, particularly park effects.
If you're up for this, post in the comments, and list good dates and times for you to draft. Unfortunately I have a lot of travel coming up (Mar. 9-13 and 16-20), but I can make just about any non-work-hours time on any other date.