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Sweeney wouldn't be ideal as a platoon hitter though. Garko is a much better fit for that role..
Its hard to see how Sweeney fits unless he can still hit and play so-so defense at 1B.. If that were the case, he'd be your main 1B.
Byrnes will likely be more productive vs LHP and he brings a glove bumping the the very productive lefty masher Bradley to DH. Byrnes Lf+Bradley DH is almost certainly an upgrade (especially when considering D) over Bradley LF+ Sweeney DH.