I would simply set your database datasets to WKID 3857 and leave it at that.
Our entire system is to big for any one projection to work well other than WKID 3857
We can import any data into that projection and it re-projects very nice. AND it lines up with ESRI Photos.
Which conveniently enough ESRI Base maps are provided in the same projection.
With out the long explanation from above how did you do it?
Our practice was to create the blank database in SDE with Web Mercator as the projection for each dataset.
Or original data was in UTM Zone 15 and it caused issues near the ends as it extended into zones 14 and 16 and was seriously warped.
When we did it we simply selected all the feature classes in the UTM dataset, and pasted them into the Web Mercator dataset. And our world was straightened out.
Robert, I'll give the straight Default setting a shot and see what I get.
The GNSS receiver documentation calls for ITRF 2008 (that's the coordinate system that the correction service uses), which is what i set in the Location Profile in Collector.
From talking to my surveyors, it could be that I have too much faith in the accuracy of the underlying ESRI basemap.