>The order above is important, local must come before existing PATHs for lower precedence so that it cannot override higher privilege bins

You've got the order reversed there - the first item found in your PATH will be used, and therefore earlier directories in your PATH have higher precedence:

  jfred@lambdacrypt ~$ cat dir1/pathtest 
  #!/run/current-system/profile/bin/bash
  echo "script in dir1"
  jfred@lambdacrypt ~$ cat dir2/pathtest 
  #!/run/current-system/profile/bin/bash
  echo "script in dir2"
  jfred@lambdacrypt ~$ PATH=$HOME/dir1:$HOME/dir2 pathtest
  script in dir1