Unfortunately, the Psaltikon isn’t available this way, since its melodies are medieval and most haven’t been transcribed into the new method. However, famous musicologist Dr. Ioannis Arvanitis has transcribed some of the Psaltikon’s chants into modern byzantine notation, which he has posted on the internet forum called “Psaltologion.” I can see if I can find some scores and post them here.
In the meantime, here is a recording of one such piece, chanted by Protopsaltis Dimos Papatzalakis. It is the Kontakion of the Ascension. You’ll notice that, although today’s byzantine music is a direct successor of the byzantine music in Byzantium, the melody is quite different than anything we would chant in church today: Kontakion of the Ascension