Thanks, guys.
I looked at the cards using Diamond Dope, and here's what I found vs. Lefty pitchers in Polo Grounds '36:
Doby’s card vs. L
BA=.278
OBP=.432
SLG=.472
Cash’s card vs. L
BA=.285
OBP=.299
SLG=.672
Burns’ card vs. L
BA=.409
OBP=.502
SLG=.577
I'm going to drop Doby to after Cash vs. L, so Cash could knock in more runs. I'm also going to look around for the extra $140,000 to upgrade my $.50m backup firstbaseman to Burns and get Burns to start instead of Cash vs. Lefties.