OK, Beernoser. It is my role to kick off Round 2 by presenting you with your first screw team. This is a serious task, and I have attempted to weigh the best approach to making this difficult for you. The rules I followed in narrowing down teams to pair with your '34 Yankees were:
1. Minimize pitching help of any kind.
2. Avoid teams with lots of cheap players
3. Hamper your final roster options in a way that forces bad compromises.
So your Yankees have a handful of solid outfielders, a few useful infielders, a very nice catcher, a couple expensive pieces you may or may not ultimately be able to use in Gehrig and Lefty Gomez, and no really cheap players.
That meant I wanted to give you a team that also had no cheap players, because you'll have to roster 6 of them. I didn't mind if they had useful outfielders or a decent catcher, because that didn't add much, and I also was darn sure not giving you any pitchers you'll want taking the mound.
So I present to you ... the 1934 St. Louis Browns.
To start, the Browns only have 19 players available to you, and you have to use 6 of them. Only one of them is under $1 million. You get 8 pitchers, none with a WHIP under 1.47 or an ERA under 4. Three of the infield positions have no backups, and two of them are pretty bad hitters. There are a couple useful bats, but perhaps one will get daggered later on and force your hand in other ways.
I'm shuddering now because I've seen all the other terrible teams and know one is coming to me, and that won't be pleasant. But at least I won't get these awful Browns. Enjoy!