In the HTM Great Horologion, in the Eclogarion section, before each psalm selection, there is a sub-title. For instance, under the Polyeleos, the subtitle is "O Ye Servants, Praise the Lord. Alleluia." (p.680) Another instance is for the birth of the Theotokos (p. 685), the subtitle is "His Meekness. Alleluia." Now, I realize that these are just truncations of the first full verse, but what is the purpose of these? Are they supposed to signal some specific melody? Or are they sung verbal cues sung by the protopsaltis or canonarch to the rest of the chanters to indicate what hymn is to be sung next? What's the deal?
Forgive me for lacking appropriate terminology in describing this.
Yes, it is indicative of the melody. You will also find this in the Octoechos (paraklitiki) where the subtitle indicates the melody that you are to sing the verses following.