In fact in the B737 you have the following time:
5' descent till 17.000', then 5' level at 17,000 feet, descent to 14,000, 30 minutes at 14'000, then descent to 10,000.
Its in the 737 Flight Planning and Performance Manal under the section Passenger Oxygen Requirements which sports a confusing and convoluted chart that may not satisfy national regulations on pax oxy requirements. You are correct in that the initial manouever must be completed as a rapid descent to achieve at least 17,000' within about 5 mins.
I am not familiar with this descent profile (certainly not in the Boeing manuals), but it may be a procedure your company has adopted and had approved by the regulator. If so, then it seems reasonable, and it certainly get the aircraft down to a safe(r) altitude quickly.
Hope you'll fly with my airline now
Happy to fly with you now.