After much testing, I think I have discovered the problem.
The table I'm inserting into has both an INSERT and an UPDATE trigger defined on it at the target.
From the source, if I just perform an insert, then replicate it, the INSERT trigger on my target table fires.
BUT....
If I do an insert, followed by an update at the source, then force replication, the INSERT trigger at my target does not fire, only the UPDATE trigger fires.
This doesn not seem like what the correct behavior should be, but that is what I am observing.