Are your points and polygons in the exact same coordinate system as each other in your NAD map?
Labels in ArcGIS Online have come a long way but will still lack full-desktop-functionality. Meaning that, they will get 'dumbed down' when they go from desktop to AGOL. It will be somewhat difficult to make everything look exactly the way you want from desktop to online, just because of the nature of this process. Sometimes, I have even "cheated" by making all my labels and annotations into actual lines instead of text and published that (but that is usually too much work).
To publish to portal on enterprise, you have to have this service (and by publish, it's the same as AGOL - a web map with feature layers that goes to a web service). Most large organizations and most government agencies have an enterprise environment where they publish their data to instead of an AGOL environment (and most use both). The benefits of it are having custom labels and symbology, different coordinate systems, you host/manage your own data, increased security, etc. to name a few. Though, it obviously comes with a higher price tag and much more maintenance/expertise.
I am not fully sure what you want to accomplish with your map but this is what I would do. I would absolutely make sure that all my data layers that I put on the web are in the exact same coordinate system (along with the map). I would only put those data layers I want to see published into my map and just publish that alone to ArcGIS Online. Then in AGOL, examine and make adjustments based on what needs to happen. I often work with surveyors who get really bent out of shape when things are "measured" properly. So, the maps I make for them in AGOL have to come with a caveat/disclaimer that it will be in WGS84 and things may be slightly skewed. I have even had to pre-load measurement data in the proper system as attributes to suffice this. Another option is to do what you did with the WGS84 map but make them separately in separate geodatabases so you don't mess the original up (and then make sure it looks good before publishing to the web).