Thanks for the pointer to nanosecond. I originally saw that and tried various things that made sense to me. For instance:
my $dt = DateTime->new(year=>$pYear, month=>$pMonth, day=>$pDay,
Well, that didn't work, since it doesn't take millisecond as an argument to new, so I tried converting $pStart to nanoseconds-since-midnight and substituting in that, but alas - it seems that the nanosecond value is only for providing the intra-second-delta.
See my above response to what I think I need to do. I'm hoping someone will show me a better way...