One thing about MLBN that hadn't occurred to me. They were assured of 2 LDS games, so it was either Nationals/Cards or O's/Yankees. It was probably obvious all along.
I think you nailed it. MLB Network had to get one game, and with 2 of the series 2-0, there was no way to guarantee a game except to take one of the series playing game 3 on wednesday. Methinks that had Cinci split with SF, that would have had the 1 PM slot. TBS gets the two not clearly necessary games at late afternoon and late night.
FWIW, MLB Network had a lot of lunch time games during the regular season. I guess they are comfortable with that slot.