This is pretty nice! You really do get the hang of using Subleq after beating each level. Although since the test cases are random, you can pass all three cases while having bugs, which also makes bugs harder to find. Regardless, I had fun squinting at lowercase letters for 30 minutes.
I was able to match or improve all of your best low-char scores (with solutions that truly work in all cases). Here are my improvements, including the code, where slashes separate lines:
| Level 4 | 8 Chars | bam/cb/a/ac |
| Level 5 | 8 Chars | da/bcm/ad/j |
| Level 6 | 10 Chars | bak/n/dbm/n/z/a |
| Level 7 | 8 Chars | cb/bam/a/ac |