In our case, all the same liturgical services, but during lockdown, wanting to encourage sense of community, we used pre-recorded readings and hymns, announcements, etc, inter-mixed with live video of priest leading service (OBS scenes). And the priest asking questions during sermon, and monitoring FB comments, enabled an interactive service (without using Zoom or similar). This was also to make service more interactive vs consumptive.
With easing of lockdown, we still wanted to be able to focus /zoom in on the priest at the alter during communion, cantor, lecters, bell ringers, choir, etc, hence a NDI PTZ camera. And having a camera that can go from alter, to pulpit, lectern, side chapel, columbarium or baptismal font in the back, etc means having a camera operator. And once you have an operator, priest no longer involved, and some OBS Scene changes (we broadcast our service bulletin beside the video), then complete automation a nice, but not need, to have. This does require 1 trained person to run the OBS computer and camera for a service, and I realize that is a blessing to be able to have such.
With a Facebook scheduled event (quick and easy to set up), and now it is even easier to create new scheduled event, as a this-year-update allows copying a prior event title/description/settings. Creating a future Scheduled FB video event only takes 10-20 seconds. Out end-of-service activities takes a few minutes, and that includes ensuring the next couple of week's worth of services are Scheduled.
But I totally get what you are looking for in terms of someone hitting a button to start stream, then another to end it, and that is it. Fixed camera position, no changing lower thirds or other overlays (other than maybe a graphic watermark?), service bulletin, etc.
Even in that scenario, possibly using FB's Scheduled event, presuming there is a fix to the auto-start issue? I see 2 challenges in such a scenario for you
1. FB's auto-start of a Scheduled Video required streaming 10 minutes in advance, so there would be some training required to accommodate that
2. and then dealing with starting stream early, but not having YT start until time/ready (ie 10+ min later)??
or maybe not worth it.
If you figured out a work-around for non-interactive Go Live with an Ad-Hoc FB livestream using their Graph API, good for you. and that probably makes way more sense for your scenario