How far ahead can you calculate?

The diagrammed position come from the David Levy book "Play Chess Combinations and Sacrifices" and was set as an exercise for a group of young players I coach. The point of the exercise wasn't to make their heads explode, but to show them that it is possible to calculate 17 or more half moves ahead, as long as you find the correct path.
To help them (and yourselves) on their way I gave them a few clues. (a) White will checkmate (b) every White move is a check (c) It is a mate in 8 if Black doesn't prolong the game through spite sacrifices.
As a group they found the first few moves in about 2 minutes, but then took another 3 or 4 minutes to get the remaining moves in the right order. Can you do better?