Zwingli wasn't making a statement that worship with instruments or corporate worship through psalmody or prayer was not worship at all. What Zwingli was against was the RCC's view that Tradition was higher than Scripture. Zwingli was a Reformer and was just as much a proponent of sola scriptura as Calvin and Luther would have been. However, Zwingli would take it a step further than both of them to say, in an attempt to distance the Reformed Church from the Catholic Church, that any form of worship that wasn't directed or commanded for the church to perform should not be performed within the bounds of directed church service. He wasn't making that statement that worship could never be performed with intruments or that it was somehow sinful to do so (as the modern RP movement would say), just that it cannot be commanded by the church if it was not commanded by Scripture.

I think that Zwingli actually would have actually leaned away from the modern RP movement because just as he was against the church commanding a style of worship that wasn't Scripturally supported, likewise we would have been against saying that one could not worship at all in a way that Scripture doesn't command against. In other words, the modern RP movement goes so far to claim that worship with instruments were tied to sacrificial practices thus sinful today since Christ was the final sacrifice. Some others have claimed that any worship with instruments would actually be rejected by God as displeasing to Him. However, if we apply Zwingli's perspective on lent that one does not have to participate given that lent appears nowhere in the Bible, there are no commands against worship with instruments in the Bible.

In essence, Zwingli's first priority was to distance the sola scriptura based Reformed Church from the tradition first RCC. It was less about what is pleasing to God and more about how far can/should the church command a certain style of worship or certain traditions. Pecedent from the OT meant little because the emulation of those styles would have still equated to tradition and not command. Even using the psalter was not commanded but recognized as mere material for liturgy and devotion but no where was it commanded to be used.

There were several reasons that Zwingli would oppose the use of instruments and singing in worship. One was that Zwingli was against was the RCC's view that tradition was higher than Scripture. Zwingli was a Reformer and was just as much a proponent of sola scriptura as Calvin and Luther would have been. However, Zwingli would take it a step further than both of them to say, in an attempt to distance the Reformed Church from the Catholic Church, that any form of worship that wasn't directed or commanded for the church to perform should not be performed within the bounds of directed church service. He wasn't making that statement that worship could never be performed with instruments or that it was somehow sinful to do so (as the modern RP movement would say), just that it cannot be commanded by the church if it was not commanded by Scripture.

I think that Zwingli actually would have actually leaned away from the modern RP movement because just as he was against the church commanding a style of worship that wasn't Scripturally supported, likewise we would have been against saying that one could not worship at all in a way that Scripture doesn't command against. In other words, the modern RP movement goes so far to claim that worship with instruments was tied to sacrificial practices thus sinful today since Christ was the final sacrifice. Some others have claimed that any worship with instruments would actually be rejected by God as displeasing to Him. However, if we apply Zwingli's perspective on lent that one does not have to participate given that lent appears nowhere in the Bible, there are no commands against worship with instruments in the Bible.

In essence, Zwingli's first priority was to distance the sola scriptura based Reformed Church from the tradition first RCC. It was less about what is pleasing to God and more about how far can/should the church command a certain style of worship or certain traditions. Precedent from the OT meant little because the emulation of those styles would have still equated to tradition and not command. Even using the psalter was not commanded but recognized as mere material for liturgy and devotion but nowhere was it commanded to be used.

The second major reason that Zwingli was against singing and instruments in worship was that he felt that worship was an inward action, a reflection and could be a distraction from true spiritual worship.

The opposition of inward and outward was an element in Zwingli's opposition to outward forms in religion. It helps explain why someone as musical as Zwingli could banish music and singing from church. Singing could distract from true spiritual worship, just as images inside church could, though not necessarily those outside. In worship as in the whole of life the glory and honor of God was fundamental. Zwingli, Huldrych (1484-1531), An Introduction to." In Literature Criticism from 1400 to 1800, edited by Jelena O. Krstovic. Vol. 37. Detroit, MI: Gale, 1997. p. 392

Zwingli led a reformation to remove anything from inside the church that could distract from true worship, but he wasn't so naive to claim that Christians couldn't use other things as reminders or helps for more efficacy, they just needed to remain outside the church.