Inspired from our Fetlar tournament these days, I have second thoughts about the Copenhagen edge & throne.
Maybe there's not a "zombie" problem here:
because the king can be forced into the open like this and captured (happened several times in the tournament):
Moreover it's compulsory for the players to move in their turn, so if white is blocked so that he cannot move, he lost for this reason.
The Fetlar edge & throne rules can be seen as logically consistent: The king must in all cases be captured from four sides by any combination of enemy pieces and forbidden squares.
Millar expresses it this way: "The white king can only be captured by being surrounded on all four sides by black warriors, or by three warriors and the throne square." ( http://www.tim-millar.co.uk/section502917_215412.html
and Uig Historical Society this way: "The object of the game, for the attackers, is to capture the king by boxing him in between four dark pieces, or between three dark pieces and his own central square, in which case the attackers win." ( http://www.ceuig.com/archives/661
Here it is not necessary that the throne is non-reenterable and non-passable. Also considering a possible next move for the king after capture is void.
It has a kind of logic to it that like the king can enter a forbidden corner square, he can also enter (reenter) the forbidden throne square. And going there, it follows that he can also choose to continue his move and pass through to another square. While only the king can stop on the throne, this passability of the throne is then normally extended to all pieces (the variants Hnefatafl 11x11, Fetlar 11x11 and Scandinavian Museums 11x11).
With the loss of the center fort option in the Copenhagen variant, the only hope left for the king when effectively excluded from the corners, is the edge fort, and this fort is easier to build when the center is passable.
Using the Fetlar edge & throne rules in the Copenhagen variant would simplify the group of 11x11 variants, as they would all have the same throne rules, and there would only be two variants of edge rules.
(See the Quick overview of tafl variants http://aagenielsen.dk/hnefatafl_rules_overview.php
In the 9x9 board variants the throne is non-reenterable and non-passable (the variants Foteviken and Ashton Lapp Tablut 9x9). This makes sense as such a throne makes the small 9x9 board topologically larger.
So, the throne rule for all variants could be reduced to:
9x9 board: non-reenterable and non-passable
11x11 board: reenterable and passable