I can't think in anything else than starting allocation more and more memory until your process crashes. Something like a loop would do it while it can print to STDERR the total allocated.

Of course, knowing how exactly to how much memory was allocated is another issue... I never tried such thing.

Doing a search in CPAN if found Apache::DProf, but I didn't saw that anything you mentioned about using mod_perl.

You could try to run your code outside Apache using Devel::SmallProf and estimate how much memory it will use at each iteration of the loop.