A. A. LeBec researched the Crucifixion in 1925 and discovered someone with hands directly overhead (as on a stake) would asphyxiate in minutes.
The cross/stake debate has only existed in the minds of JWs. An actual dispute is whether the patibulum (cross piece) was on top of the stipes (upright pole) or lower; either resembling a majuscule or minuscule "T". Another question was whether the nails were through the tops of the feet into the front of the cross or through the sides of the feet into the sides of the cross.
The Watchtower has completely ignored all evidence that disagrees with them on every subject, so far. Why would they change now? They even use an illustration from De Cruce Liber Tres by Justus Lipsius to indicate support for a stake being used for Jesus' execution. In reality, several different images 
are in the book of various methods of Roman crucifixion and only the one copied in the NWT appendix indicates a pole. Lipsius did not support the idea of Christ dying on a stake.
Of course, when all this evidence is compiled and introduced to the average JW, they'll start to waffle and deny the object used makes any difference. Of course this is a lie, since JWs generally start arguments about it, believing they can win because the average person has done no research on the subject. The JW is relying on being the only one in the argument with any information (even if it's completely false). It's only when they lose, they backpedal and deny it's of any consequence. Also, if the device isn't important, why go against all conventional understanding and make a big deal out of it for the last 50 years?
Because the GB requires JWs to grant complete authority to everything said by the Society. If there is any question in the JW's mind, one sign of weakness in their brazen statements in the literature, the slightest realization the "faithful and discreet slave" might not have any clue what they're talking about, the entire mystique of the Society and its position over the laity could completely unravel. For some JWs, it does completely unravel.
are in the book of various methods of Roman crucifixion and only the one copied in the NWT appendix indicates a pole. Lipsius did not support the idea of Christ dying on a stake.