Our company policy states that after 80 kts the take off becomes GO ORIENTATED and the only abort should be for
* fire or fire warning
* engine failure
* unsafe configuration
* if the airplane is unsafe or unable to fly
Remember with a blown tyre you are going to have reduced stopping capability and tyre debis might also have caused damage to the anti skid system and hydraulics which is going to complicate the situation and increase the possibility of an overrun. Rather continue the take off, keep the gear down and assess the situation once airborne. Plan to land back on the most suitable runway available. Identifying the tyre failure seems to be the biggest problem. Havn't had one but I think acceleration should be very close to normal and there might be a swing which should not be to difficult to control on aircraft with more than one wheel per bogie.