Camera not updated with latest hmd pose if rendering to a RenderTexture

In our game, we have a stacked camera setup (for near/far mono rendering) where we have a camera that renders to a rendertexture and with a custom projection matrix. The problem is that it does not follow the VR headset correctly (its view matrix is slightly off), unlike the camera without a rendertexture. This makes the overlayed image jittery and needs correction. Also, any camera that renders to texture is forced to render before normal cameras regardless of depth value. Is this to be expected?

Another "quirk" is that when you call camera.Render() inside OnRenderImage, OnPostRender, etc, that camera ignores its stereoTargetEye and inherits the settings from the event camera.

While we have been able to work around this limitation, it would be much better if it worked right out of the box.
This is tested with 2018.3. All info welcome.