I feel a bit stupid here... I spent half the day banging my head for solutions, went to a birthday party for 4 hours, came back and wrote the above post, and suddenly the solution came to me!
Get Component: Collide Object (GameObject) then store RigidBody (Object)
Add Component: Use Owner, select FixedJoint as Component and store as Object
Set Property: Target FixedJoint (Object), set connectedBody as RigidBody (Object)
Rinse, Repeat!
Tested and works perfectly! It's so simple and I wasted so much time! Sigh...
Closes eyes and whispers: "Game development is fun. Game development is fun!"
