You can escape the Space Rig with an Underhill

1. Grab an Underhill and drink it
2. stand on top of the arcade cabinet
3. when you grow again, jump and vault the wall behind the cabinet. Sometimes it helps to stand still and jump/vault.
4. you’ll fall under the floor - you can run around through the walls or drop through the big triangular gap under the barrel game tunnel and as long as you land somewhere on the rig frame you can run around out there.

If it catches you too far out of bounds, you’ll be teleported back to your pod.