... the initial goal of getting the tests to run has been met.

I'm looking at your  $test_7: (0, 0, -60) -> (-1, 59, 0) (result: -1° 59' 0"). (There's a similar test 7 here with result (-1, 59, 2).) I would have thought the normalized or reduced result to be  (0 -1 0) (0° -1' 0"). If the required result shown in the code is correct, it suggests a set of sign propagation rules I have yet to see. Can you expand on this?

I notice that you haven't recast your core code into a module yet. Doing so is a good idea for many reasons, including testing. Note that Test::More::use_ok() is available for modules and Test::More::require_ok() for more humble files.

The other point that occurred to me is also in terms of general design. Rather than always reduce()-ing deg/min/sec tuples to other d/m/s tuples, it might be less of a headache to normalize d/m/s tuples to, say, integer or decimal fraction arc-seconds (or maybe radians?) or whatever's most convenient, do all the trig in these standard units, then convert back to the ultimate d/m/s (or whatever) output form just once as a final step. Just a thought...