As a former USAF Physiological training instructor, in a training field where we trained pilots, flight nurses, aircrew members,VIPS, guests, etc., the medical affects of altitude on the human body, I probably went through close to a thousand rapid decompressions in hypobaric chambers. We called them RD's....and normally in my days, rd chamber flights simulated an actual decompression from 8k to about 22-25k.. Been away a long time, but I would suppose the training profiles are much the same.......yep. you dont have to clear your ears on the way up, but you do on the way down....sinuses are another matter...I have seen some painful sinus problems with both trainers and trainees.
and in regard to the supplemental oxygen systems aboard a 777, I am totally un-informed, but in my passenger flight history aboard commercial airliners, I have seen "walkaround" bottles stowed in some aircraft...btw, we used them all the time out of Kadena back in the day...while pushin leaflets out the backend of a HerkyBird over North Nam, unpressurized with the ramp down at fl250 give or take a few...usually around 0200 or so local....with an ECM bud about 10k overhead, paintin a hundred radar targets on NV scopes..
Along with the medical oxygen, the AC would also contain PBE for firefighting. Those contain 15 minutes worth of oxygen, but that is a hood you wear over your head again, pretty difficult to attain and get into within 10 seconds before hypoxia.
And yeah, I know what you mean about utilizing oxygen bottles. It truly is the cure for
ahem
exhaustion. Personally, I preferred just slipping up to the cockpit and taking a hit off theirs. Nothing to write up. ;-)