Be a Captain! Assume the authority and accept the responsibility! Judgement is what we get paid for, because we can teach monkeys to flick or depress a switch.
As for the A320 overweight landing procedure being an abnormal, of course it is, but it amounts to a landing vertical speed of no more than 360fpm (if memory serves me), which is no big deal. No special maintenance action needed thereafter. As for the landing distance, not sure what the 737 manual says anymore, but ALL performance factors are based on a set of circumstances, which, in the case of a depressurization, would tend to suggest you have considerably greater landing capability than the conditions listed for the landing calculation.
For those who seem to think landing over MLW is a huge deal, it is done with some frequency in regular line operations all over the world. However, as has been said over and over, with the authority comes the responsibility, so one has to ensure that landing margins and conditions merit not waiting for a lower landing weight. Also, in the example, it appears that one does not NEED to burn all 7,000kgs of fuel, as one is only trying to get down to the "factored" landing weight that creates a legally suitable hard surface. Again, I emphasize that I do not remember the normal landing conditions (braking, reversers, spoilers, anti-skid, etc..), but usually you have one or two of these systems in your back pocket to reduce (sometimes vastly) landing distance. One last thing, if the 737 is like the 320, then MANUAL braking considerably reduces required landing distance over auto brakes, so I would be standing 'em up, if needed!
