Would I proceed the way that your example states even if I didn't pay any income taxes?
Wasn't aware of how the process went, nor did anyone at the church I pastor. I just became Pastor in 2018.
I was paid $400 per week beginning in February, and $100 per week before officially taking over as Pastor.
If you want to DIY your payroll, I highly recommend you look at using Gusto! It is very user friendly and their support is awesome! Plus they know how to set up and maintain payrolls for churches and nonprofit organizations.
Note: I am a "partner" of Gusto, but as I have told you before ... I never recommend anything that we or our clients have not tried and love =)