Dear fellows oversees,
I know: it's your game, we got it from you and we shall not change it.
However considder this.
In the OP is written BU is in C, with 2nd and 3th ocupied. Now BU
ALWAYS have a bad angle on 1st.
That's why we, at least in the Neth.'s, are in B in this situation. Now we only have a difficult job to do on a pick-off on 3rd. There are a lot less calls on 3rd than on 1st in this situation. A matter of math...
Best of all is a 3-umpire crew!