1) Hi Eagle, I'm afraid you misinterpreted the cklist: you turn the recirc fan off not because in doing so you will hide the problem (not recirculating air thus not seeing the smoke generated somewhere else), but because in this particular case the recirc fan is the source of smoke.
2) You set 10000ft to make the cabin climb at 10000ft, thus dumping more air overboard.
10000ft is the maximum before having to use crew oxygen.
I agree with you a higher altitude would be even better, if you are already on oxygen masks... but not 14000ft, as you don't want the passengers masks to be deployed with smoke in the cabin.
Maybe 13000ft....?
Cheers