Used to park at Boston Latin School, but that was for the '04 ALDS. Took the train from Riverside Station for WS Game 2 that year, but not in the lot (See below).
Last time I was at Fenway was the week before my wedding (I've been married 9 years). My sister-in-law had a garage pass at one of the hospitals. Riverside is going to be swamped. There were occasions where I had to park in a neighborhood on the other side of the overpass and walk to the station.
You may want to try a stop a couple stations up the D line toward Fenway, or try a different color line and connect to a non-A Green line outbound.