Here are the steps I am doing to publish a web map which I want to be my base map using my spatial reference - NOT esri's
I added a new map and added my data with my spatial reference
I click on Share > Web Map
Share As Web Map window opens
I give it all the required <bleep>
I click Analyze and I get an error because the cache spatial reference does not match the map spatial reference (00079)
I click on Configuration
There I see two options
I select on <WebMapName>_WTL1
I click on Properties icon
it opens the configuration settings for the WTL1 features
I click on the Configuration tab
I click the pencil next to Tile
I see the error and see that the Tiling Scheme is using "ArcGIS Online / Bing Maps / Google Maps"
I cannot change the tiling scheme.
But when I publish a web layer (not a web map) to tile, I am able to modify this to my liking (my own tiling scheme with my spatial reference) - not so when publishing a web map
How do I change this setting so I can create a basemap as a web layer using my spatial reference?
You are correct with your last point you will want to publish a tile layer with your desired parameters to Arcgis Online.
Once you have published it to ArcGIS Online you can follow the below blog to create your own custom basemap gallery including using the imagery that you have just published as a basemap.
Additionally, if you are publishing large amount of data you should use the recommended workflow found below under the subsection "Publish large tile packages"
Thanks for the detailed reply and the helpful links. I should have mentioned that I'm using AG Enterprise, not AGOL. In reading your links, it seems to me there are so many options (and so little time).
I'm afraid there is no solution to change the Tiling Scheme when publishing a web map from ArcGIS Pro. The software must assume all data is in "ArcGIS Online / Bing Maps / Google Maps."
