Of course you recognized that you are managing a high risk airway (re-do thyroid operation with known pre-op L RN paralysis). You also promptly performed tracheostomy.
There are many details regarding this case that are pertinent. First, recurrent nerve injury (retraction, dissection, etc.) is easy to do. It is important during the case to treat the nerve with respect (both in the neck and mediastinum). Second, are you sure the nerve is out? You also described laryngeal edema. Leaving the endotracheal tube in overnight will probably increase laryngeal/glottic edema. So, I would not have left the tube in overnight. Extubation in the OR is ideal; you are set to do a trach if needed.
When you extubated the patient the next morning, there are some maneuvers you can do that may decrease the need for trach. (1) deflate the cuff (and occlude the lumen of the endotracheal tube) and see if the patient can ventilate "around the tube" while leaving the endotracheal tube in place; (2) nasopharyngoscopy can provide more info (larynx vs glottic problem); (3) extubate in the OR is always an option; (4) in the OR, you can sedate the patient and look at the cords (and of course do the trach, if necessary); (5) to minimize risk of bronchospasm, you can spray the cords with lidocaine; (6) if the problem is laryngeal edema, then there is a role for steroids, head elevation, and diuretics; and (7) from your description of the case, I would not have tried using difficult airway tools (stylet, bronchoscope, etc), but favor "rapid sequence," followed by trach.
I think the most important aspect of your case is that you recognized a difficult airway situation, were prepared to do a trach, then quickly recognized that a trach was indicated and consequently did it. However, by the "tone" of your presentation, you suggest that next time you will have EVERYTHING ready in the event that a trach is needed.