Split roads in network by polygons

[HarrySmiles]

I have a road network that I need to divide up by custom geographic areas. The network uses the below connectivity and elevation policies. The FromNodeID and ToNodeID are just sequential numbers with no real elevation value.

Connectivity:
  Policies:
    Streets edges use End Point connectivity policy.
  Elevation Model: Elevation Fields
    Streets: FromNodeID, ToNodeID

What I tried to do was to intersect the streets feature class with the geographic areas, then use this as the edges in the network. The issue is that the connectivity breaks at all the cut locations. Is there a tool that I can use to do this work?

This an example of the road network in green with the custom areas in black.

and this is an example of where the cut has occurred. The red dots are the current junctions, and  blue dots are the ones after the cut. You can see from the labels that there is now a vertical connectivity issue, but I have no idea how to fix this in an automated way, and doing it manually is unfeasable.

Any ideas how I can go about doing this? 

[MelindaMorang]

If your streets are already in a network dataset, then certain special behavior kicks in when you edit them that will help maintain network connectivity.  This includes correctly updating the Z-level fields in the child features of a split feature.  However, if the network dataset isn't created yet and you're just editing an ordinary feature class, these rules will not apply.

You can read about the special editing behavior for features participating in a network here: https://pro.arcgis.com/en/pro-app/latest/help/analysis/networks/network-dataset-street-editing.htm

As far as splitting all your features at once, using one of the standard editing tools is your best bet since that will ensure that the special network behavior occurs.  This page might give you what you need: https://pro.arcgis.com/en/pro-app/latest/help/editing/clip-features-using-another-feature.htm