In a situation where a converted organist is unavailable, and it is felt strongly that the organist/musician(s) should be converted, the congregation should go a cappella.
This will have the added beneficial effect of reminding the congregation that the singing is the element of praise, whereas the musical instrument is at best a circumstance, for the sake of man, and teach them something more about the Divine priorities in worship, according to the RPW revealed in Scripture.
At the very least he Lord indicates nowhere that He is displeased if musical instruments are left out, or that He insists on their use for proper NT worship, so why should anyone be concerned if they have to do without them for a time; or if they believe for some reason that this circumstance of worship should not be provided by an unbeliever, why should they compromise their conscience for the sake of some musical accompaniment that the Lord does not demand or require, and that is not necessary for the congregation's sake. The instrument(s) being absent, may even encourage them to work and improve on the element of praise, the singing, because the blemishes and inadequacies in the singing aren't masked by a lifeless instrument, that the Lord, to put it no more highly, has no interest in.