In considering the use of congregational song in worship, it is needful to remember the point of worship. Different traditions may answer this question in different ways; I speak from the denominational tradition in which I work, and those who read this should consider these points in light of the tradition in which they work (and if you don't know what that tradition has to say, there's a homework assignment for you).
Continuing with the PC(USA)'s Book of Order, specifically the Directory for Worship, section W-3.01 opens up to a broader outline of the church's worship, offering an order for that worship while taking pains to clarify that this is not the only possible order of worship. Section W-3.0103 offers up the claim that the offered order of worship "seeks to uphold the centrality of Word and Sacraments in the church's faith, life, and worship." For those in, say, Episcopal and Lutheran traditions, there probably isn't much to make clergy blink, but we in Presbyland have to hesitate for a moment, as this cannot be said of many churches -- the Word is there, but the Sacraments are largely absent unless (a) someone is being baptized, or (b) it happens to be that one Sunday of the month the church practices the Lord's Supper.
I have no answer for this. Some Presbyterian churches manage to partake of communion weekly; most, I'm guessing, don't. Nor am I sure that congregational song offers any help here. I suppose one could sing a communion hymn even if communion isn't being taken in that worship service, but that feels a little passive-aggressive.
Nonetheless, the idea of the centrality of Word and (even absent) Sacrament in worship still has ramifications for the practice of congregational song. Do the songs or hymns we sing support and point towards the proclamation of the Word and the sharing of the Lord's Supper?
One doesn't have to be a practitioner of any particular worship style for this trap to be sprung. There are no doubt parishioners who go to contemporary worship (whatever that means) services only to hear the band do its thing, and check out on pretty much anything that happens otherwise. There are (I know this for fact) parishioners who go to traditional worship (whatever that means) services only to hear the organist tear it up on hymn or anthem or prelude or postlude, or to hear the professionally-supplemented choir knock out some Mozart or Mendelssohn, and check out on pretty much anything that happens otherwise. Neither is a desirable or even acceptable result. Neither really encourages a focus on the centrality of Word and Sacrament, and in fact are quite likely distractions from those central features of worship.
As to where in worship congregational singing might be most appropriate, that answer might well be "anywhere." Something at or near the beginning of the service is particularly appropriate, and typically a hymn or song will appear at the end of the service as well; other places might include in or around the reading of scripture (a sung psalm is particularly appropriate here) and, at least in this pastor's opinion, following the sermon. Yes, that's four possible hymns or songs in worship. Remember, they're more likely to remember one of those than any particular thing about your sermon. Swallow your pride and get your congregation singing.
Get them singing, though, with an eye towards what matters most in worship: the Word proclaimed, and the sacraments given and received. If the congregation's song is not pointing towards these central tenets of worship, then they are frankly distracting from worship (remember, not every experience, not even every spiritual experience, is worship), and may be doing more harm than good.
Just something else to think about, dear pastor.
This guy is great, really, but he's not the point of worship.