If the water is coming in UNDER the threshhold, that is
probably where the problem is.

Yep, makes sense...

What's strange is the leak is right in the middle of the door. Until
yesterday, the space on both sides of the door were open (to the interior)
and were completely dry. If the exterior flashing was incorrect, or the
caulking along the sides was failing, I would think the leak would tend to
come in along the sides. But, I know water can travel in strange paths
sometimes.

Can't see your door from here

Yeah, unfortunately, without tearing things apart again I can't see it
either. I didn't take photos along the way because I didn't expect any
problems.

the threshold is sitting higher than you thought and
did not get bedded in the caulk.

It's possible. Oddly, I left drainage on the outside, but sealed the
inside. In theory, any water getting in should drain out, but it's seeping
under the interior caulking instead. I verified the subfloor was level
before installing the door (actually had a very minor slope outwards).
That's what makes me think the water is coming in at the sides and running
down BEHIND the caulking I installed under the door.

how much drop is there from the front edge
of threshold to the porch surface outside?

About 4-5 inches right now. We will be rebuilding the front steps and
landing this summer when things dry out again and the new landing will be a
couple inches lower.

Thanks for the advice!

Anthony