You seriously don't have TOK wrenches in your tool set yet?
Top of Keyway (TOK) wrenches use the top of the keyway instead of the more standard bottom of keyway (BOK) wrenches.
FACT: I picked locks for DECADES before TOK wrenching was discovered. Once I started TOK wrenching, many locks I'd previously failed to pick - I picked.
My success rate more than DOUBLED.
If the proof is in the pudding, TOK wrenches are a gigantic, delicious chocolate pudding, with whipped-cream on top.
The startling reality is, many of the lock picking issues you're having could be because you're tensioning from the Bottom of Keyway which restricts your access.
Now the secret has been revealed, you can successfully pick more locks.