It surprised me to realize that we've never had an Angels team represented in any of the first five seasons of Twist w/ a Hero. I spot a couple of viable options using the October baseball sub-theme.
The 1983 Angels roster features Luis Tiant, Fred Lynn, Reggie Jackson, Rod Carew and Bobby Grich. The 1986 and 2002 rosters aren't bad either. But the one that really excites me is the 2014 Angels. That roster features Albert Pujols, Mike Trout and Josh Hamilton on offense, and several low WHIP/low OAV pitchers that could be used to make an unconventional, but effective, pitching staff... especially if you added a the 289 IP/.99 WHIP that 1976 Frank Tanana provides.