We split the target 24 15 14 13 12 11 10 9 16 23 22 21 20 19 18 17 1 8 7 6 5 4 3 2 into the three segments generated by A8, A6, and A4:

1. A8 must yield 24 15 14 13 12 11 10 9 (originally 24 13 12 9 → insert 15 14 after 24 and 11 10 after 12)  
2. A6/A7 must yield 16 23 22 21 20 19 18 17 (originally 16 23 22 21 20 18 17 → insert 19 between 20 and 18)  
3. A4/A5 must yield 1 8 7 6 5 4 3 2 (originally 1 8 6 5 4 3 → insert 7 between 8 and A5, and 2 at the end)  

This uses only terminal insertions, totaling 7 new symbols.

Updated production rules:
rule_4: A4 -> 1 8 7 A5 5 4 3 2
rule_6: A6 -> 16 23 A7 21 20 19 18 17
rule_8: A8 -> 24 15 14 13 12 11 10 9