Ahhhhh! This is a horse of a different color! Now you're talking!
There is a great distinction between Peter Jon-Gilquist's music and that of Arvo Part.
Arvo Part, like Tavener, is a modern composer who is Orthodox and has written music for liturgical purposes (at least I think they both have). Those settings will not be used in liturgies unless approved. They were written with the Orthodox musical traditions in mind. Obviously, a lot of Part's work will not because it is either Latin or secular. Most of his works were commissioned and are heavily influenced by his faith. Some of Part's work uses the choral tradition within Orthodoxy (I'm using that term very lightly) to inspire a piece. That does not make it fit for liturgical purposes any more than Resanovic's "Collateral Damage for Clarinet and Orchestra."
Peter Jon-Gilquist's music does not generally follow the Orthodox liturgical traditions. They are folk-pop in style and are designed for use outside liturgical settings. I think this music is fine. I don't know about other traditions, but I know that very old Georgian folk music blends Orthodox theological concepts into everyday life. That doesn't make these folk songs liturgical. It simply means these people were living their faith to an extent that it merged with there other concerns.
I think the same is true for classical works. Would a devout Orthodox believer integrate his faith into his work? Of course! No less so than, say, Philip Glass.
I suppose it's like a painter who is Orthodox. Sometimes they may paint things that are not icons, but have religous themes. That doesn't mean they are good or bad, but they aren't fit for liturgy.
One has to remember that these composers are typically not theologians. They are subject to the same mistakes and corrections as the rest of us.
I admit that I have a copy of "Living in an Orthodox World: Singable Songs for the Young and Young in Heart." It is rarely listened to at our house, although my son is only four. Part, on the other hand, is played almost weekly. I have a copy of several of his pieces at work. If you like it and it isn't bad, listen to it. If there were a group of guys who liked punk and they started a punk band and they were all devout Orthodox and they weaved Orthodox principles into their loud, two-minute tunes, I don't have a problem with it. Maybe they'll compose one of those great prayers that gets used at church. But the music should stay outside liturgy.