Longest *fairy* chess problem

Question

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.

Answer 1

Is there a clear definition of what constitutes a "fairy" problem? For instance, if you can stipulate a change to the dimensions of the board, then solutions of an infinite length could be devised. Here's an amusing example of such a "dimensional" puzzle:

Answer 2

On request, here is the problem: SCHWALBE 324-2, Article "Die Valladao-Challenge" by Jochen Schröder, p.389, Nr. 5, by Jochen Schröder, help-aim square h8, 2+59, in 720575940379279357 moves, conditions Antigrid, king dynasty, shortestmover w, diagram anticirce Cheylan w, sentinelles generalises en, noires wb, and black pawns everywhere except ws a5, wk b3, empty a1 h1, bb b1 c1 f1 g1, bk d1, drop hole e1. Solution implements a waiting queue and I won't type it here, see article.