Cheer Up, I don't fly the 737 but these are my generic thoughts on a landing gear problem.
- Go-Around! at some point advise ATC and request vectors to somewhere nice and quiet.
- Carry out the appropriate non-normal checklist in consultation with maintenance watch if available.
- Go back and land if all the wheels are down.
- If not, make a decision on where you want to land.
- Advise ATC (organise fire services, require XX runway), Company, Cabin Crew and Cabin (Pax). Nice calm briefing required to both cabin crew and pax.
- Jettison fuel as required to reduce landing speeds.
- LAND.
My belief is that you can land quite safely with various gear configurations. Of course, you're going to get sparks and fairly serious scrape marks on the paintwork but the aircraft should maintain its structural integrity without too many dramas.
As to whether it's legit or not to have one pilot at the controls, in a situation like this it's largely up to the PIC to determine what's legit or not. Command judgement in an emergency situation is paramount and most docs/ regulations will include a disclaimer to that effect in Non-Normal situations.
Any additions??