Baseball is my favorite sport, but I would be totally fine with cutting the season back to 140 games. You could start in early to mid April and still end in September. Maybe even have a shorter timeframe if you have Saturday doubleheaders. That accounts to an average of 25 games a month which would allow teams more time to rest and travel if they have doubleheaders and allows more dates for makeup games. I like the idea of expanding the league by two so there could be 32 teams, or four divisions of 8. Each division winner make the playoffs and the divisional series could be best of five and the championship and World Series could be best of 7.
As for the draft, I'm not sure what I would change with it to be honest, though if a few teams seem to be tanking (I think there is a difference between tanking and selling off parts for a rebuild), then maybe have a draft lottery like the NBA. I like the idea better for the NFL, but it could work for MLB. While regulation would sound like a good idea, I don't know how it would be implemented. If say the Tigers have the worst record, who replaces them? Some MILB team that's stadium is 1/3 the size? Say that MILB team is an affiliate of the Dodgers, then what? The Tigers would have no MLB representation and the Dodgers would then have two teams. Even if a Tigers affiliate replaces them, then they would just send all their best players to that team. It would cause too many problems.
Maybe a better decision would be if a team is accused and found to be tanking on purpose, then take away future draft picks and/or fine the owner. Again, I think there is a difference between selling off parts and tanking to get picks. I also think there is a difference between tanking and being a penny pincher owner. While I don't like them either, I don't know what you can do besides find a way to groom potential new owners to step in if it is persistant.
Moving onto the field, I don't like a lot of the new rules, and I don't like creating a bunch of new ones. I do like the idea of limiting time outs for batters, it seems a lot of them stall more than the pitchers. I would shorten the time for a replay to be called too. Five seconds and make it a player/manager decision (no waiting on someone to tell them).
I would also change the extra innings rule. I still don't like the runner on second, but if they want to have it, then I wouldn't start a runner on until the 11th inning, and the runner would start on first. If they make it to the next inning or beyond, then the runner can start on second. I don't mind the 7 inning double header, but would only implement that if it was for makeup games and they were back to back games (not a day/night doubleheader).
As far as fan interaction, I like the idea of creating more opportunities for fans to meet with the players and would try to create more opportunities for those interactions especially on weekend and summer day games. I wouldn't make it mandatory, but I think it would be nice.
I'm sure there are other rules I'd create and some would probably alienate new and old fans alike, but I would also make some of these changes as quick as possible (at the start of the next season), and would try not to make more rules unless absolutely needed.
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In the process of updating my collection so don't trust any of my lists right now.