I second this, using gst-launch, you can run a gstreamer pipeline in one line in the terminal that generates a hardware h264-encoded stream that you can tune to any bitrate. Something like this:

  gst-launch-1.0 rtpbin name=rtpbin rpicamsrc preview=0 bitrate=4000000 do-timestamp=1 ! 'video/x-h264, width=1920, height=1080, framerate=30/1,profile=high' ! h264parse ! rtph264pay config-interval=1 pt=96 ! rtpbin.send_rtp_sink_0 rtpbin.send_rtp_src_0 ! udpsink host=YOUR_IP port=YOUR_PORT rtpbin.send_rtcp_src_0 sync=false async=false

Gstreamer should include rpicamsrc directly nowadays for your convenience.

I'd be love to hear more about how you did it! I found streaming (and restreaming) RTP fairly straightforward but annoying to setup with gst-launch (there seems to be no simple option to get an SDP file out, apparently you are meant to lovingly handcraft one from the debug log).

But I couldn't figure out how to stream RTSP, especially not in a way that would preserve NTP timestamp information when restreaming (for synchronization with other streams). There is gst-rtsp-server, but as far as I can tell the idea is that you use it as a library to build your own custom server code.

Is there a simple way I was missing?

This is the comment I was scrolling for. GStreamer is awesome.