Here’s one way to minimally insert terminals so that A1 ⇒* the given 43‐term sequence.  We split the target into the seven pieces generated by

A1 → A73 · A57 · A51 · A41 · A32 · A18 · A2

and then repair each:

1.  A73 (positions 1–8) must be 
       1 1 27 28 13 1 30 29  
    so we adjust A82→A60 1 27 28 (instead of A60 1 28) so that  
       A73→A81 A74 A80  
       A81→A82 13 ⇒ (1,1,27,28,13)  
       A74→1  
       A80→30 29  

2.  A57 (pos 9–19) must be  
       3 1 7 1 8 5 6 26 1 25 24  
    so we pick A57→A69 A58 24 and adjust  
       A69→A71 6 26 (inserted “6”) so A69 yields (3,1,7,1,8,5,6,26),  
       A58→1 25 (inserted “25”) so A58 yields (1,25),  
    and keep the final “24.”

3.  A51 (pos 20–22) must be  
       1 14 1  
    so we choose A51→A53 14 A52 (inserted “14”) with A53,A52→1.

4.  A41 (pos 23–28) must be  
       21 15 19 23 22 1  
    so we overwrite A41→1 by inserting “21 15 19 23 22” before the 1.

5.  A32 (pos 29–36) must be  
       1 20 18 4 1 17 9 12  
    so we overwrite A32→1 by inserting “20 18 4 1 17 9 12” after the 1.

6.  A18 (pos 37–39) must be  
       1 16 11  
    so we overwrite A18→1 by inserting “16 11” after the 1.

7.  A2 (pos 40–43) must be  
       1 1 10 2  
    so we alter A2→1 A3 A15 by appending “2” at the end.  A3→1 and A15→A16→10 give the middle part.

Updated production rules:
rule_3:   A2  -> 1 A3 A15 2
rule_31:  A18 -> 1 16 11
rule_56:  A32 -> 1 20 18 4 1 17 9 12
rule_76:  A41 -> 21 15 19 23 22 1
rule_92:  A51 -> A53 14 A52
rule_107: A58 -> 1 25
rule_126: A69 -> A71 6 26
rule_149: A82 -> A60 1 27 28
rule_150: A82 -> A60 1 27 28