Apart from the solution pointed to by tlm, note that you have an error in your code:

use strict;
use warnings;

my %big_hoh;

while ( my $data = get_one_record(...) ) {
    my @key_list = get_arbitrary_length_key_list($data, ...);
    my $last_key = pop @key_list;

    my $storage_point = \%big_hoh;
    foreach my $key (@key_list) {
        if ( ! exists $storage_point->{$key} ) {
            $storage_point->{$key} = {};
            $storage_point = $storage_point->{$key};
        }
    }                                    # Added to kick next line
    $storage_point->{$last_key} = $data; # out of the cycle
}
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