Ok what I'm trying to do is create a table where football tactics counter each other in a numbered order. Such as like a filled in order of the below table...

This can be simplified into a 7x7 matrix table such as the below (by renaming the tactics, 1-7)

We have 3 rules that need to be adeared to:
1) There needs to be a different tactic in each row and each column. Essentially making like a sudoku puzzle.
2) Rows can't have the same 2 numbers reversed. i.e. 6, 7 should not be 7,6 elsewhere

3) Every number entered needs to have it's opposite entered. i.e. if Attacking is 2nd strongest vs Balanced, then Balanced is 2nd weakest vs Attacking. Here's an illustrated example...

I've been using this to assist me KenKen Solver, however it doesn't take additional rules 2 & 3 into consideration.

Is this solvable?