Your compass will not point true north (in most locations). It can be off as much as 20 degrees, well more than your bean angle.
google "magnetic declination". Maybe you should stick with the beam angle of 60 degrees, if you can't sample the reception strength for the fine tuning.
I still don't think altitude will help any. What angle difference do you expect there, 5 degrees? If it is not more than 30 degrees, forget it.