One pawn is sufficient for helpmate.
A bishop plus a knight is sufficient for helpmate.
A king plus bishop can deliver helpmate if the other side has at least one piece which can limit the king's mobility without stopping the bishop check and without checking the other king, so knight or bishop of the other colour.
Similarly a king plus knight can deliver helpmate if the other side has a bishop or a knight.
A lone king cannot deliver mate.
Any major piece is sufficient for helpmate.
Castling is irrelevant for helpmate. En passant is only relevant in blocked positions and castlingplayers are irrelevant for helpmateobliged by 11.11 to help the arbiter in such situations.
In any case: I cannot come up with examples which are hard helpmates of any length, but I am in no way an expert when it comes to helpmates.
Helpmates of arbitrary length are always trivial because it is either just a case of the mating side queening a pawn and mating or it is just a matter of one side getting rid of the right material and moving into position to be mated. What is difficult is helpmate in a set number of moves.
Perhaps one way to make the job for the arbiter difficult is to not keep track of previous moves
This is nonsense!
Article 8.1.1
In the course of play each player is required to record his own moves and those of his opponent in the correct manner, move after move, as clearly and legibly as possible, in the algebraic notation (Appendix C), on the ‘scoresheet’ prescribed for the competition.
As an arbiter when I see somebody not recording the moves I first ask them to bring their scoresheet up to date with all the moves. If they refuse I impose a time penalty. Repeated refusal results in loss of the game.
Note also article 11.11 of the FIDE Laws of Chess:
Both players must assist the arbiter in any situation requiring reconstruction of the game, including draw claims.