Longest *fairy* chess problem

Longest orthodox chess problem

One for the specialists. In the newest SCHWALBE I saw some titanic lengths (one problem had 2^59+2^57+3 ~ 10^18 moves!) As you see, this scales with O(2^(n^2)), where n is the chess board length. Which is rather puny to what might be possible, e.g. a problem scaling with the Ackermann function. Anyone knowing the current record holder for any fairy chess problem, no holds barred, only uniqueness of solution is required?

EDIT (due to comments): You can have an arbitrarily-sized board or sneak in infinity via new pieces. In this sense, the answer is "infinity". So I should better ask for an actual, printed, stipulation of the form "Something happens in n moves", where you "just" have to beat the above value. In the Dawson example, the possible infinity is stated (and the first n values on largers board are given in a reprint - I know this problem from there), but these printed n are of course <<10^18.

• Almost certainly the record holder is the problem that you sketched vaguely in the question. Please post details of that as an answer Commented Jan 11 at 1:08