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?
[FEN "K1k5/P1Pp4/p2P4/Pp6/P1p5/2P5/8/8 - - - 0 0 "] 1. axb5 axb5 a6 b4 cxb4 c3 b5 c2 b6 c1=Q b7# 1-0
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.