A few quotes from the Rabbi on 'Traditions of the Fathers'
in which he says that the prayers of each tribe rise up through the tribe's own special gateway
There are twelve windows in heaven corresponding to the Twelve Tribes. The prayers of each and every tribe rise up through the one gateway that is unique to it…There is no doubt that were the prayers of all the tribes equal, there would be no need for the twelve windows and gateways. But each gateway has its own approach, as it should, and since their prayers differ, special gateways for each and every tribe are necessary. Prayer resembles the roots and source of its souls, and it is therefore appropriate for each and every person to keep the custom of the order of his prayers, in keeping with the custom of his forefathers.
Kaf HaChaim, section 63