I still want to dwell a bit on this "absudly earn the right to repeat". How bad is it really that people can repeat, if it is not for the purpose of attacking? Note that I did not propose that a player who was attacked can do any move he wants; he can only make a repeat with the piece that was attacked, or perhaps interpose another piece on the line of attack. These will almost always be purely defensive moves. So yes, you will often have the right to repeat without a real reason, but you cannot do much with the granted moves in terms of attacking. Besides, having the right to repeat is one thing, having the opportunity to repeat quite another. When there are futile attacks as side effects, these will in general be ignored, and 'evading' them would never lead to a repeat, as they were not evaded before.
And what we aim to prevent is that one player can force repeats one-sidedly, through attacks that can only be reasonably evaded in one way. If both players aren't interested in making progress, a repetition ban cannot cure that. Even with a few pieces there are so many ways in which you can pointlessly shuffle them without repeating that you can last a lifetime.
Can you think of an actual example of a perpetual chase that you would have liked to be forbidden, but that would be allowed because the attacker derives the right from futile side-effect attacks of the defender's move?
BTW, I have to extend my proposed rule such that you are always allowed to move your King, even when it was not in check. Otherwise dead draws like K vs K could be won by forcing stalemate through repeats. Which I think would be undesirable.
As to the case of mutual perpetual attacks, how about this rule:
* A 'forced evasion' is a move with a piece that suffered a new (possibly futile) attack, or a move onto the ray over which such an atack passes.
* It is only allowed to repeat a position through a forced evasion, except:
* It is forbidden to cause a repeat when all the moves leading from the previous occurrence of that position to the current one are forced evasions.
This puts the burden of deviating from a mutual chase on the one who started it. Which seems reasonable, as he was not forced to start it.
"Would it really be a problem if there was always complete freedom in moving pieces that just got attacked?"
I was initially very hesitant to do a classification of pieces, as someone who is mostly against assigning piece values. However, the rest of the rule as it's written wouldn't work without it. Admittedly, there are times where it's perfectly reasonable to attack (with intent to capture) pieces normally thought of as much weaker, purely for strategical purposes, with no fewer than a dozen such instances in my own games.
Complex tactical reasons and strategical reasons for such attacks still evade the scope of my rule. I am aware of this. For those reasons, I supposed that whoever set up such an attack would deserve to profit from it.
To allow freedom to repeat for all attacked pieces, important or not, would greatly provide players a way to absurdly "earn" the right to repeat, even when clearly the opponent does not have attacking intent. Thus, I felt it more prudent to allow players who truly feel they must defend to judge for themselves, providing a means by which to actively remove pieces from attack where the rule does not explicitly cover it, which encompasses the vast majority of concerns. This is one of the main reasons behind my declaration mechanic.
I could add another attacking criterion...