FFF
If the fire is an engine fire and is outside the cockpit, then the best thing to do is descend, 45 deg AOB and at just below Vne, this will give you a high vertical and forward speed and hence the best chance of blowing the fire out (and getting down quickly)!
If the fire is in the cockpit (i.e. an electrical fire) you don't want to fan the flames, so you descend at just below Vfe with full flaps, this will give you a high ROD but a low forward speed so you don't give the fire more oxygen to burn.
As for the other subject in discussion, S-turns or side-slip would be my preferred way of dumping height in order to hit my aiming point, IMHO fewer variables to misjudge.
(Edited to say this)
As a stress/design engineer I can unequivocally say that Vfe is a structural limit (not a motor limit) and you do run the risk of breaking bits of the aircraft if you put flaps down at higher speeds.