Here's how you're getting the head across the river into the socket.
Pull the lever as usual (tether hold the lever, point to the floor release)
As soon as the head is down, configure your grappling hook to:
- Air Lifter (loadout "high")
- Upgrade your loadout B Mods (do more missions to upgrade) to:
- Helium: Gas
- Armor: Indestructible
- Locomotion: Guided
Then, tether 3-4 Airlifters onto the head. With the Locomotion: Guided on, you can steer the head now with your center aim. It goes when the center aim is.
If the head is stuck somewhere, just point a bit up to the sky and it floats higher.
Steer the head over the bridge to the socket.
Once there, release all tethers and Retractor tether the head into the socket.