you instructor has a point.
you cant do autoland cause the ap has to be diengaged by 500ft.
however if you do divert to you alternate you will be restricted to FL200 plus the additional burn off. depeneding on how much fuel you have you might not be able to make it to the alternate. you will have to make a decision based on the fuel.
this scenario happend in acutal life with an indian airlines A300, i think. they ended up crash landing cause they didnt have enough of fuel to make it to the alternate. im sure someone else could shed some light on this particular incident.
cheers.