Move all the deformation bones into one armature, and the controls into the other. Think of it like this.
The Control rig moves the DEF rig, and the DEF rig moves the mesh.
Bake the animation onto the DEF rig and then export that to Unity. So you will only have 1 rig in Unity (I actually don’t know very much about Unity sorry, Gonzo handles that side of things)
To move all the deformation bones into a second rig just duplicate all the bones that actually do the deforming, (shift+d) and separate them into a new armature (p), then join that armature with your existing spline armature. (ctrl+j) Then add a “copy transforms” on all these new bones to the same bone in the control rig (use python for that so you don’t go crazy)
This is advanced stuff so if you struggle to understand, don’t worry that is totally normal!!