There are two definitions of forced in play here:
Forced as in it the only legal move.
Forced as in you are bound by the rules of chess to make a move, i.e. your king is in check or it is your turn to move.
While there is some overlap between the two definitions, they are still separate categories in general. Here are records for each one, with and without promoted pieces.
Each record shall be recorded in length by plies, or half-moves, Since a player has a choice of what piece to promote to, promotion is not considered a fully forced move under definition #1.
One Legal Move, No Promoted Pieces-15 Ply
[Title "Bernd Schwarzkopf, Feenschach 1980 On Page 13"]
[FEN "8/2p5/2p5/1pP5/nP3p2/PP2B3/1pp1p3/brkbK3 b - - 0 1"]
[startflipped ""]
1... fxe3 2. bxa4 bxa4 3. b5 cxb5 4. c6 b4 5. axb4 a3 6. b5 a2 7. b6 cxb6 8. c7 b5
Source: The Die Schwalbe Chess Problem Database
Additional Source: A PDF of the original source
One Legal Move, Promoted Pieces-18 Moves
[Title "Karl Scherer, Feenshach 1980 On Page 13"]
[FEN "BQ4R1/2Q5/3Q4/4Q1pp/5B1P/6QK/Rrrrrrrq/R4nk1 w - - 0 1"]
1. Qxh2+ Rxh2+ 2. Bxh2+ Rxh2+ 3. Qxh2+ Rxh2+ 4. Qxh2+ Rxh2+ 5. Qxh2+ Rxh2+ 6. Qxh2+ Rxh2+ 7. Rxh2 g4+ 8. Rxg4+ hxg4+ 9. Kxg4
Source: The Die Schwalbe Chess Problem Database
Additional Source: A PDF of the original source
Multiple Legal Moves, No Promoted Pieces-12 Ply
[Title "Noam D. Elkies, Tim Krabbe’s Website Diary Entry #267 2004 (Version By Me)"]
[FEN "KBk5/P1P1p2p/2PN3P/P6p/2p3rP/2P3pB/6P1/8 b - - 0 1"]
[startflipped ""]
1... exd6 2. a6 d5 3. Bxg4+ hxg4 4. h5 d4 5. cxd4 c3 6. d5 c2 7. d6
Source: Diary Entry #267
Multiple Legal Moves, Promoted Pieces-22 Ply
[Title "Alexey Khanyan, Tim Krabbe's Website Diary Entry #267 2008, Mate In 11"]
[FEN "4Q2Q/4r3/4n1n1/1bbK1krn/RR1RR1RR/2qn1R1n/4n1nN/Q3Q3 b - - 0 1"]
[startflipped ""]
1... Ng2f4+ 2. Rfxf4+ N2xf4+ 3. Rgxf4+ Nh3xf4+ 4. Rhxf4+ Ndxf4+ 5. Rxf4+ Nhxf4+ 6. Rxf4+ Ngxf4+ 7. Rxf4+ Nxf4+ 8. Rxf4+ Kxf4+ 9. Qee5+ Qxe5+ 10. Qaxe5+ Rgxe5+ 11. Qxe5+ Rxe5+ 12. Qxe5#
Source: Diary Entry #267
Here are records if you want each one to end in checkmate.
One Legal Move, No Promoted Pieces-11 Ply
[Title "@Peter, Chess Stack Exchange 3/11/2015, Mate In 6"]
[FEN "7k/q5Q1/p4PPK/6PP/8/5P2/8/8 b - - 0 1"]
[startflipped ""]
1... Qxg7+ 2. fxg7+ Kg8 3. f4 a5 4. f5 a4 5. f6 a3 6. f7#
Source: This CSE question.
One Legal Move, Promoted Pieces-16 Ply
[Title "Bernd Schwarzkopf After Karl Scherer, Feenschach 1980 On Page 13, Mate In 8"]
[FEN "1KN4r/QRRRRRRr/kq6/p1q1R3/PP1q1b2/4q3/5q2/1r4q1 b KQkq - 0 1"]
[startflipped ""]
1... Qxa7+ 2. Rxa7+ Qxa7+ 3. Rxa7+ Qxa7+ 4. Rxa7+ Qxa7+ 5. Rxa7+ Qxa7+ 6. Rxa7+ Qxa7+ 7. Rxa7+ Rxa7 8. b5+ Rxb5+ 9. axb5#
Source: The Die Schwalbe Chess Problem Database
Additional Source: A PDF of the original source
Multiple Legal Moves, No Promoted Pieces-14 Ply
[Title "Noam D. Elkies, Tim Krabbe’s Website Diary Entry #267 2004 (Version By Me)"]
[FEN "KBk5/P1P1p2p/2PN3P/P6p/2p3rP/2P3pB/6P1/8 b - - 0 1"]
[startflipped ""]
1... exd6 2. a6 d5 3. Bxg4+ hxg4 4. h5 d4 5. cxd4 c3 6. d5 c2 7. d6 c1=Q 8. d7#
Multiple Legal Moves, Promoted Pieces-See the above Alexey Khanyan problem.