Surely with damaged engine cowlings, descend as quickly as possible but perhaps not at Max speed?
Assuming the B737 is like other Boeings the procedure for a Rapid Descent is to descend at VMO/MMO unless structural integrity is in doubt. How you determine structural integrity is an open question. I would suggest that if there is ANY doubt then limit airspeed.
Boeing tell us, I work as an instructor for Boeing in the UK, that with engine severe damage the vibration will be severe. It is not something we can replicate in the simulator because the amount of vibration would cause other problems apparently. We are assured that you will have no doubt that there is severe vibration!
During conversion and routine refresher training both Engine Severe Damage Separation and Depressurisation exercises are flown. Both events require prompt memory actions. What is unique(?) in this event was that both situations occurred either simultaneously or very close together. That puts a great onus on the crew to prioritise their actions which are made more difficult wearing an oxygen mask which, without doubt, makes communication between crew (sound of O2 through the intercom and restricted ability to look at your colleague directly, almost like wearing horse blinkers) more difficult.
It would have been a situation requiring excellent CRM in such a challenging situation.
It makes me cross in all the reporting that the reference is to 'the pilot'. Undoubtedly her co-pilot was an essential part of the operation to ensure a safe outcome.
With reference to the RT used it must be remembered that the USA has a slightly more laid back approach to RT than perhaps those of us in Europe. Listening to the transcripts there seemed to be no doubt that the seriousness of the situation was understood by all concerned. Had the crew thought otherwise they probably would have broadcast a Mayday call. Certain parts of the world I would say it would be essential!
Well done to all involved.