Would the amateur recital Battlefield be able to move a Baron Nashor at the Baron Pit Battlefield back to base?

No, Amateur Recital cannot move Baron Nashor to its base.

According to the rules and the retrieved RiftJudge FAQ #8771, Amateur Recital's ability requires you to select a specific unit to move, which counts as "choosing" that unit. Because Baron Nashor has the ability "I can't be chosen by enemy spells and abilities," he is an illegal target for Amateur Recital's ability.