Chris
I've been intending to reply but just juggling a lot of tasks. this will be brief, will probably need more discussion.
Yes you need to reprocess unless you're publishing in ArcGIS Online - in the web we can apply a simple vertical offset.
you said "3D maps" so I assume you mean the mesh and/or point cloud? if you mean the DSM/DTM then adjusting a raster is different, and does NOT need to go through reprocessing (although that may be advised).
Last, do you expect precise Z alignment, or are you just seeking to get close enough to the default Esri world terrain so the drone products are visible and not obviously 'floating'?
Have you tried adding control points from the map? That extracts Z values from the default Esri world terrain but if you're in an area of natural vegetation I appreciate finding the correct (x,y) is a challenge and you don't want to shift your data horizontally with a sloppy control point...
Can you let me know the original vertical offset (before you attempted adjustment)? It may be the difference between ellipsoidal (GPS) vs. orthometric height for your site, based on the quality & settings of GPS from your drone. if true, that's a method to analytically determine the Z offset
Cody