Hi webreake,
This article mentions several Axis cameras “(which natively support H.264): M1011(-W), M1031-W, P3301(-V), Q1755, Q6032”: Re-streaming an RTSP stream through Wowza Pro (RTSP/RTP)
It’s not push, but at least you don’t need to use VLC to transcode.
I believe the Haivision Barracuda hardware encoder can push an RTSP mpegts stream to Wowza. So, if you hooked an analog camera to one of those, it would do what you want.