The issue I would take with the Reformed RP is that it is unduly Biblicist. That is to say, it assumes that the gospel, as witnessed in Holy Scripture, will always demand and evoke the same response, and that this response is itself set out in Scripture. I think the internal evidence of the Bible is against this view, at both a surface and a deeper level. On the surface, it is clear to me that the NT does not intend to give a manual for worship, and nowhere claims to prescribe the structure or content of our gathered meetings. (As an aside, it is ironic that the chapters which come closest to doing this - the instructions for use of gifts in 1 Corinthians - are substantially laid aside by most advocates of the Reformed RP!) At a deeper level, Scripture presents a gathering in of a diverse, multi-tongued people, each bringing the firstfruits of their own culture in worship. It does not tie itself to first-century mediterranean forms, and nor should we.
The proper role of Scripture in relation to corporate worship, in my opinion, is that our worship is to be shaped and controlled by the gospel which is witnessed and proclaimed in Holy Scripture. (In other words, the role of the Bible as a regulatory authority moves one step back in the process, from regulating the worship service directly to regulating the understanding of the gospel which in turn regulates the service).
This does not set the Church free, as in the Anglican model, to derive ceremonies and rites which are considered to be "indifferent, and alterable". Rather, it sets the Church free to ask the question: what does the gospel demand of us in worship, here and now? This will, of course, lead to alterable forms and actions. But they are altered by the demands of the gospel, not the will of men. In this way, our worship will be guided and ruled by the gospel of Christ, and therefore by Christ himself.