Is it possible to hear a piece in Finale in just intonation using the "human playback" mode and the built-in Garritan orchestra? If not, what is the best way of doing this, other than live performance? This piece is for a string quartet, arco and pizzicato.
To the best of my knowledge, Finale and its sound libraries do not support anything other than 12-tone equal-temperament at A=440 Hz.
However, you can purchase the full version of the stand-alone Garritan Personal Orchestra program and use it with Finale in place of the built-in Finale sounds. Garritan Personal Orchestra's ARIA playback engine can be used in any tuning scheme according to the Scala protocol.
This would not provide you with 100% pure just intonation as it would be played by a live human string quartet; rather, it would enable you to tune 12 notes in an octave to any scheme of mean-tone tuning, such as those used on harpsichords in the Baroque era.
This would be as close as you could get to just intonation using Finale.