Just to reply to my answer in case someone is interested in doing something similar.
Without access to ArcGIS Enterprise and ArcGIS Server, this is probably the best solution:
You will need to set up a GeoServer instance that will serve your data from Postgres. Use GeoServer to create WFS or WMS services, which can then be used in MapViewer and of course all other applications within AGOL that use a webmap. If you've never worked with WFS/WMS within AGOL, this is probably the best place to start.
I tested this workflow and it generally works pretty well. Just keep in mind you won't be able to edit the data saved in Postgres through AGOL.
It is a bit fiddly process, but it can be done if required.