Andrew,
I'm not unsympathetic to your concerns. It's likely true that many who include instruments do not have a thought through defense of their position, just as many bring their children for baptism without necessarily having a proper understanding of why they should. Good defenses of the use of musical instruments are thin on the ground, for good reason. No one on that side of the argument thinks their opponents are "denying the sufficiency of Christ's sacrifice", so they do not feel the urgent burden to challenge the other side that is understandably felt by the "musical instruments are unbiblical" side. Building a proper argument, as for baptism, is not a one verse or one passage task; it involves a proper understanding of the relationship of church and temple (which is the primary OT background for the church, not the synagogue), and an ability to interpret the law properly, dividing rightly between moral, civil, and ceremonial worship. We are not anabaptists, who consider it a sufficient argument against something that "That's OT worship", although too often Reformed arguments sound very like that - mainly because most of the things wrong with Rome are rooted in OT categories (priests, sacrifices, sacred buildings, etc). The bare assertion that because something is linked with temple and sacrifice, it therefore has no more significance for us as Christians today is simply false. Otherwise, we lose singing itself, which was not part of the synagogue service and become Sydney Anglicans, gathering for edification only, not exaltation. Nor does something have to be reiterated in the NT in order to guide our behavior for us today.
I contend that musical instruments are not ceremonial law (otherwise they would have to point forward to Christ in some recognizable fashion). They are not moral law, or they would always have been part of worship - and the tabernacle has neither instruments nor singing. They are part of the civil law - which means that their general equity continues to guide our behavior today. Obviously, that argument would need to be substantially fleshed out, something I don't have the time or inclination to do here, knowing I will be immediately inundated with 15 responses for people who disagree. It's perfectly fair for people to respond, but equally, it's not my calling to spend a lot of time interacting in internet comboxes, which are not ideal for complex theological discussions. Normally, I abstain from these discussions on the basis of a sense that the returns don't justify the use of my time, which would be much better served working on my magnum opus on the Biblical Theology of Worship (seriously, I've been working on this off and on for 25 years, and hope to publish it someday, but it requires a comprehensive knowledge of everything - OT, NT, CH, ST and PT - so it is a daunting task). But I have several other volumes to complete before I can seriously develop this material further.
One further mistake that often clouds these discussions is the assumption that if the OT law on instruments is still valid today, then instruments - the same instruments that David commanded - would be mandated. This first of all misunderstands the RPW, since there are several elements of worship (lawful oaths, sacraments) that are sometimes present and not always so. In the same way, instruments could be affirmed without being required. Second, it is defused by the argument that instruments are civil law; the details expire, but the general equity continues. So the law requiring a parapet around the roof of a person's house has relevance for modern building codes but doesn't have to be literally still a requirement.