Sorry, nodo you have any suggestion on higher end HDMI → RTSP converters,
This thread was the first time I looked into such technology, and I have no experience with them.
I've just come across a number of no-name/low-cost devices (various technology) that have poorly written firmware and next to no support. In a volunteer situation like yours, stuff needs to be durable and just work (ideally for really cheap).. but cheap and good rarely go together, so my approach is to search for a good deal on quality, supported gear. ymmv
Then again, the HC-X2000 appears to a very nice camera (and with a quick look at manual) to have a built-in RTSP transmitter... unfortunately works over WiFi 2.4GhZ only... but at least capability built-in and supported. I have the idea of using WiFi (I haven't looked .. but a USB3 to Ethernet adapter would be such a better option.. but I digress) a PoE-powered 2.4GhZ only Access Point (AP)? might work at 25/30fps with AP security configured to ensure NOTHING else can use the connection (gets into whole WiFi beaconing/bandwidth issues with stupid user tricks (ie when people/companies configure their devices to auto-connect to any available AP, like bicycle computers riding by)... ideal setup might be something where you configure AP to use MAC filtering, etc to only allow cameras to connect, and ignore all else?
if you could get this instead, it appears the Panasonic AG-CX10 has built in ethernet.