scanscanscan,
careful here. I think you would be considered unwise to abort for a tyre failure prior to V1. Prior to 80 knots fine, as stated in my Boeing QRH (NNM1.1), but prior to V1 is a little more dodgy. Boeing (NNM 1.1 again) say above 80 kts reject for engine failure; fire; or, if the airplane is unsafe or unable to fly. The Boeing video on RTOs specifically says NOT to abort for a tyre failure above 80 kts (I accept that other things may cause damage that might requiire an abort). However, you are 'off-piste' if you do abort. Exactly at the moment when you need all the braking available to stop in the available field length you have reduced braking because a tyre is not available - you may be answering the questions from the overrun/ditch!
Now reading between the lines I suspect the guy driving the console was implying that if you had left the gear down, checked with the tower whether a tyre had burst on the runway or not, and then returned to land, most of the problems would not have occured (presumably your 'god' has considered broken tyre whizzing around the gear bay may cause some hyd lines to rupture with odd consequences).
Now, if you are stuck in that situation I can agree with everybody!(flaps best set for min speed if GA not a problem, but what speed would you use, and should we really be making the speeds up?).
However, you are not in a rush. Does anybody know if Boeing provide a service on HF or for your ops to call to get more advice in such circumstances?
Regards.
av8er