In Attic and Koine Greek, προσκυνέω is just as likely to mean "worship" (i.e. worship befitting a god) as it is anything else.
This is the case in the LXX and NT. For example, John 4:23: ἀλλὰ ἔρχεται ὥρα καὶ νῦν ἐστίν, ὅτε οἱ ἀληθινοὶ προσκυνηταὶ προσκυνήσουσιν τῷ πατρὶ ἐν πνεύματι καὶ ἀληθείᾳ, καὶ γὰρ ὁ πατὴρ τοιούτους ζητεῖ τοὺς προσκυνοῦντας αὐτόν.
So, to answer the OP, there are many parts of the liturgical services that use προσκυνέω in its older, pre-Damascene (and Scriptural) sense, possibly because these hymns predate the Iconoclastic period. In addition to the example you cited, which is actually a direct allusion to the language of the Psalms, there is the hymn that the clergy chant during the Little Entrance of the Divine Liturgy. Also, IIRC, the Pentecost prayers, which predate the Damascene. There are many others.
That aside, it's my feeling that the modern English words "worship" and "veneration" imply a far greater difference than their equivalents in Byzantine & Modern Greek, Romanian, etc. That's largely because "veneration" is essentially meaningless in our cultural vocabulary, but also because, in English, we are constantly trying to defend Orthodoxy against modern-day Iconoclasts.
In modern Greek, however, you can still speak of η προσκύνηση (worship) at church, and a person can indeed προσκυνεί God. Theologians, of course, will speak about η Λατρευτική προσκύνηση, but even that is telling, no?