I'm no expert in TBC, I've had my own frustrations. I'm not sure what you mean by "ground" coordinates. Maybe that the GRID is scaled up to ground. I've taken to do my work using LDP's where the scale factor is calculated to, in effect raise the grid plane to near ground (not ground coordinates but grid coordinates that are very near to ground in elevation). That way your GRID coordinates would be about ground.
Of course if you want to maintain the bearings from the SPC then you'd either need to use an oblique projection or maybe you could set the central meridian at the same location as the SPC.
Anyway, all this is the reason I all but stopped using SPC's years ago. Using an SPC base system to survey in ground coordinate is just to ridden with issues. But that's just me, I might do it in a way that is not standard, I don't know.
I believe there should be a way for the TGO file to be converted correctly. You may need to get some help from Trimble, especially since you have such a large amount of work.
Is there a scale factor to ground from the TGO file that doesn't make it through to the TBC file? You probably already hunted for that.
If you keep at it I think you will find out what the issue is, it's frustrating I know. It's hard to learn a new way when you are used to doing one way. TBC appears to me to be almost a complete new way. It's not just an upgrade to TGO but mostly a whole new system and way of doing things. It's almost like switching from AutoCAD to MicroStation. TBC does have some very nice new features. There are some features of TGO that just aren't there anymore in TBC. That's frustrating also.
Keep playing around with some little files as I suggested and you'll probably figure it out and then be able to do what you want with the total conversions.
Once you are certain you have ALL the settings absolutely correct, project, local site settings, (a window should open on the right), click in the northing window, click on the point that you want to scale from, (the northing and easting fields will populate), click in the elevation field, click on the point again, check the box to compute the ground scale factor, choose the points you want to scale-if not all of them, click ok. now export the points.