I cannot speak about different regulations but JAR - OPS1 in fact asks for livable altitude before O2 runs out (less than 50% pax, let's keep it simple) that is 14000 and once it is gone for 10000 ft in thirty minutes. I get a feeling that other regulations sound similar.
Hence you have 42 minutes to get to FL100 but have to manage FL140 before pax oxy runs out. However the scenario you suggest still asks for a very demanding profile. If someone wanted to fine tune this extremly improbable case I would suggest investing in more detailed maps to get you out of FL220 sooner.