MilesTag IR communication protocol
The following is mentioned on the MilesTag Data Protocol page (the original version of the protocol) that also uses the same timing:


  The MilesTag data packet consists of a header pulse followed by 16 data bits (two 8-bit data bytes) and 1 parity bit.  The header pulse and data bits are encoded onto a 40kHz infrared carrier signal using pulse-length modulation. This modulation is identical to the format used in Sony IR remotes and others.


So I suspect the original design decision was to pick a low-level encoding method known to be compatible with a wide range of IR receivers. You seem to have determined that the receiver you're using can demodulate a signal in ten cycles, so I don't see a reason in principle the higher data rate won't work but the following might apply:


It may be less reliable in one regard because you're giving the receiver less time to demodulate the signal.
In another regard it might be more reliable because the shorter packet length will allow less time for player movements and obstructions to interfere with the packet.


It may just be one of those things you have to try and see what difference it makes in practice. If it were me for a start I'd write code so the transmitter pulse duration could be easily changed using a few buttons and LCD, and on the receiver end do the same. Then you could also use the LCD to display the numbers of packets received over a known period of time to determine the packet loss percentage at various data rates and under different conditions.

Another idea somewhat "outside the box" is that if you're coding your own protocol then you could add a rolling sequence number to the packet. If you received two packets with consecutive sequence numbers you could assume when in "minigun" mode that it represented say three hits. Of course depending on the length of the sequence number you'd have a certain probability that you'd hit the next sequence number by chance at a later point rather than it being a consecutive hit.