C (gcc) -zexecstack -Wl,-eA -nostartfiles on Linux x86-64, 876 bytes, score 798

A[]={1111+1111+1111+111+111-11-11-11-11+1+1+1,1111111111+111111111-11111111+1111111+1111111-111111+1111+1111+111+111+111+111+111-11-11-11-11+1+1+1+1+1,111111+111111-11111-1111+111+111+111-11-1-1-1-1-1,111111111+111111111+11111111+11111111+11111111+1111111+1111111+111111-1111-1111-1111-1111-111-111-111+11+11+11+11+1+1+1+1+1,1111111111+1111111111-111111111-111111111-111111111-111111111+11111111+11111111+11111111+11111111-1111111-1111111-1111111-111111-111111-111111+11111+11111-1111+111+111+11+1,111111111+111111111+111111111+111111111+111111111-11111111-1111111-1111111-1111111-1111111-111111-111111+1111+1111+1111+1111+1111-111-111-111+11+11-1-1,1111111111+1111111111-111111111-111111111-111111111-111111111+11111111+11111111+11111111+11111111-1111111-1111111-111111-111111-111111-111111-111111-1111-1111-1111-1111-1111+11+11+11+11+1,11111-1111-1111-111-111-111-11+1+1+1};

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Charset: A[]={+,-1};

Same method as the previous answer, with even more hacking to supply a custom entry point named A (which has the smallest ASCII value among a-zA-Z_. Credit to this SO answer.

Assembly: (NASM syntax)

bits 64
global _start
_start:
  mov edx, 13
  pop rax
  push rax
  lea rsi, [rel s]
  pop rdi
  syscall
s: db "Hello, World!"

Uses the argc=1 set up on the stack to load the value 1 to rax and rdi. The instructions are slightly mixed up in order to get the minimal code length in C.

Here is the Python script that generates the "ones decomposition" from the xxd -i output (C include-style hex output) of the compiled binary.

C (gcc) -zexecstack on Linux x86-64, 891 bytes, score 1154

main[]={1111+1111+1111+111+111-11-11-11-11+1+1+1,1111111111-111111111-111111111+11111111-1111111-111111-111111-111111-111111+11111-1111-1111-1111-1111+111+111+111+11,1+1+1+1,111111111-11111111-11111111-1111111-1111111-1111111-1111111+111111+111111+111111+111111+11111+11111+11111+11111-111-111-111-111-111-11-11-11,1111111111+1111111111-111111111-111111111-111111111-111111111+11111111+11111111+11111111+11111111-1111111-1111111-1111111+111111+11111+11111+11111+11111-1111-111-111+11+11+11,1111111111+111111111+111111111+111111111+11111111+11111111-1111111-1111111-1111111-1111111-111111-111111-111111-111111-11111-11111-11111-11111-11111+1111+1111+1111+1111-111-111-111-11-1-1-1-1,1111111111+111111111+111111111+111111111+111111111+111111111+11111111+11111111-1111111-1111111-1111111-1111111+111111+111111+111111+11111+11111+11111+11111+11111-1111-1111-1111-1111-111+11-1-1-1-1-1,11+11+11};

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Uses ceilingcat's minimal Turing-complete charset main[]={1+,};, plus - to meet the code length limit.

Assembly: (NASM syntax)

bits 64
global _start
_start:
  mov edx, 13
  lea rsi, [rel s]
  mov eax, edi
  syscall
s: db "Hello, World!"

Essentially calls write syscall once, and goes into arbitrary instructions formed by the string literal, causing segfault.