Sounds like the phone did its job and got you back safe, so maybe the lesson here is simpler than buying more gear. A second light means a second thing to forget to check, and now you're carrying two dead lamps instead of one. You said yourself the real fix was checking the headlamp in the parking lot, and that does not cost anything. Cold hands and a dark pack are what kept you from finding the spare batteries, so practice finding your stuff with your eyes closed at home instead of adding more stuff to lose. Half the people I hike with carry three lights and still get caught out because none of them got tested until it mattered.

That math only works if you swap radios on weekends too.

Yep, I do the same thing and honestly the sketchy part is half the fun. But here is the thing your wife is missing: the ship will actually wait for you if you booked through them, so the real question is whether your own two feet can get you back before the gangway pulls up.