Good work in trying to use surveying techniques in Field Maps / TMM.
Have you seen the link below? Can you create a geoid file from your local site?
https://community.trimble.com/viewdocument/how-to-side-load-custom-geoids-f?CommunityKey=2724bc18-0f...
This may not be all that's needed but you could test it. We still have the coordinate system that's assigned to the map (and its layers).
I'm not a Trimble fan, but the TSC5 does allow you to run GIS software (Field Maps) and survey software such (Trimble Access) on the same device. I understand that a screen rotation app is needed to make Field Maps work in landscape mode. Trimble won't license the Android version of Trimble Access on a non-Trimble device, otherwise we would have a lot of devices that could be used.
It might be wise for us to ask for integration of GIS and survey. Yeah, we get improvements in drips and drops but why not integrate Trimble Access with ArcGIS Online?
@JoelCusick/ @JoelCusick1 - do you have your ears on? Joel may be able to help.