I am looking for positions from where every move is forced up to a certain depth. If the original position (or one in between) occurs again, the sequence is finished there.
You mean like this?
[Title "Vilhelm Röpke, Skakbladet 1942, Mate In 6"] [FEN "K1k5/P1Pp4/1p1P4/8/p7/P2P4/8/8 w - - 0 1"]
White mates in 6.
I guess that's 9 consecutive forced moves. It would be eleven except for black's choice of promotion piece on his fifth move. I don't know if it's a record, and I don't know who composed this classic chess problem.