Of course, if I invented a system that was resistant to manipulation, there'd be much rejoicing. But this goal seems still far away if at all possible.

It's not hard to fix a system so that it is resistant to manipulation: given a set of players, compute how the players would want to modify their utility functions under the original system, then use the original system on the modified utility functions to pick an outcome, then make that the solution under the new system. In the new system, players no longer has any incentive to modify their utility functions.

Of course if you do this, the new system might lose some desirable properties of the original system. But since you're assuming that the players are self-modifying AIs, that just means your system never really had those properties to begin with.