eman7400 - you can color me crazy, but for your 3rd team I am gifting you a World Champion: the 1930 Philadelphia Athletics. The A's have a few studs but most of them, particularly on the hitting side do not add much from what you already have with the 1940 Tigers and 1970 White Sox. Al Simmons at $10.3M is great if you can afford him. Jimmie Foxx is an excellent piece but so is Rudy York. Mickey Cochrane would be your best catcher, but you've already got some good options to mix and match with Tebbetts, Sullivan, Herrmann and Josephson.
The A's pitching only offers 7 to choose from. Of course there is Lefty Grove, but at $10.3M? Earnshaw could give you 300+ innings but he's pricey and not the same caliber as Lefty. The rest of the staff, all 5 of them, is not as bad as many of the others from 1930, but they are still flawed.
Last, for whatever it is worth, I almost took these Athletics with the 2nd pick in the first round and then using Lefty Grove until his arm fell off. Shows you what I know...