That could work, but an added nuance is that every year I ask people to re-confitm in the thread they are all set to play. I do that around the beginning of December. Sometimes a person drops out at that stage. So I would want to wait until after that before finalising your 1-4, 5-8, 9-12 proposal in case it needs to be tweaked slightly and only agree in principal for now. I also think we might want to tinker a bit. a make it 1-5, 6-9, 10-12 so there can be more choice of letters for the last round master. Although wee have eliminated X and Z, letter Q is a dead end street and U and V are pretty useless as well. All the other letters are reasonable.
I have also thought of making 12 pre set pairings to pick from using roman numerals to define them. The very best letters paired with the dead end letters or with no letters like you have suggested.