Okay, I can live with PerlTidy wanting to dictate line length, but what fresh hell prevents it from aligning that string on the new line with... at the very least, the innermost enclosing for loop? Ideally, it would be aligned with the or die on the previous line

The default maximum line length Perltidy uses is 80 columns ( though not cast in stone ), as stated in the Perltidy documentation.
However, you can change that like so:
perltidy -l=85 perlscript.pl Please, note the -l=85.
Given, the OP preferred format, the CLI command work for me to produce the format you want:

perltidy -b -i=3 -l=90 perlscript.pl
[download]

Please, see EXAMPLES under Perltidy documentation.

Note, I will advice you don't go beyond between 72 to 82 columns line length except you know what you are doing (ofcourse you do).
Another option is that, you can reformat manually after using Perltidy or what about that?