Strange... Or more likely I don't understand what is going on here, being a noob. Your suggestion about using the epochs helped me at least figure out a way around my problem. If I add:

$oldtime = $oldtime - $ctime->tzoffset;
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I get the desired results, although my statement

print "The old time is $oldtime\n";
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Then prints a formatted time 6 hours in the future. I needed to update that to

print "The old time is ", $oldtime + $ctime->tzoffset, "\n";
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To get it to print the correct time. That isn't a great concern as I actually won't ever be using the print statements, only the calculations, in the bigger script I am retrofitting. Still, it shows I am missing something basic in how this all works and that concerns me.

Note: where I am tzoffset is -21600 (-6 hours, CST).

And further illustrating my noob-ness, I didn't include the entire updated script so it actually made sense. Sorry. Here it is:

use strict;
use warnings;
use Time::Piece;

my $ctime = Time::Piece->new;
my $oldtime = Time::Piece->strptime('Dec 19 17:44:00 2016', '%b %d %T 
+%Y');

$oldtime = $oldtime - $ctime->tzoffset;

print "The current time is $ctime\n";
print "The old time is ", $oldtime + $ctime->tzoffset, "\n";

my $halfago = $ctime - 1800;

print "Half an hour ago is $halfago\n";

if ($oldtime > $halfago)
{
    print "Old time is within a half hour\n";
}
else
{
    print "Old time is outside a half hour\n";
}
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