I did already have in mind a solution to your last question: in all such cases, the lowest number takes precedence. In your example, 23 would continue from 02 rather than 03.
Here's where things become more difficult. By looking at an empty tesseract illustration, I'm able to plug in face designations and work things through. While 02 and 03 are Territory Faces of 01, so are 12 and 13. Like with 02 and 03, the edge they share in common is the left file of one and the right file of the other, and this edge also borders on 23. However, the edge of 23 it borders on is perpendicular to the edge that 02 and 03 border on. So, if 02 and 03 bordered it along a file, 12 and 13 would have to border it along a rank, or vice versa. This means that ranks and files will sometimes border each other along a common edge.
Maybe if you start Territory Faces with the edge appropriate to the edge of the Home Face is starts on, things will work out more easily. So, instead of putting Pawns and Spears on the first two ranks, do that for only two, and put them on the last two ranks for another two, on the leftmost files for another two, and on the rightmost files for another two.
Here's where things become more difficult. By looking at an empty tesseract illustration, I'm able to plug in face designations and work things through. While 02 and 03 are Territory Faces of 01, so are 12 and 13. Like with 02 and 03, the edge they share in common is the left file of one and the right file of the other, and this edge also borders on 23. However, the edge of 23 it borders on is perpendicular to the edge that 02 and 03 border on. So, if 02 and 03 bordered it along a file, 12 and 13 would have to border it along a rank, or vice versa. This means that ranks and files will sometimes border each other along a common edge.
Maybe if you start Territory Faces with the edge appropriate to the edge of the Home Face is starts on, things will work out more easily. So, instead of putting Pawns and Spears on the first two ranks, do that for only two, and put them on the last two ranks for another two, on the leftmost files for another two, and on the rightmost files for another two.