{ Shudder...}

There seem three flavours of post-v6.1 FBX rigging: 'IT WORKS !!', 'Breaks to multi-rig', often crippled as you describe, and 'SPLAT' aka 'ST:TOS Transporter Accident'...

A lot of the issues seem to stem from Blender's ever-evolving FBX plug-ins. If you look at rig 'shapes' in eg free 'Open 3D Model Viewer', the three flavours soon become apparent. Worse, an artist may craft two similar models a few months apart but, due to differing plug-in versions, one may have 'Full IK' and be a sweetie, while the other won't play nice...

And then, I'm told, there's the 'MakeHuman' FBX rig, which is a law unto itself...

I'm still at 'BoxMan' rigging level, so I wish your project well.