Forgive me if this is a simple answer on a missed detail, I'll blame late Friday, but I'm sure it's on me.
Can you not add a second probe from Netpath? This screenshot shows I have two pollers (one is my primary and one is my APE) going to the same destination. If you click the plus you should be able to add additional probes to the same service (path):
If that's not it, I think this is the part I'm confused on:
"I find I cannot do this monitoring in one instance of Solarwinds because NetPath doesn't see a difference in monitoring by source APE when the destination address and port have already been used once elsewhere. I realize I could set a different destination port, but that's not the preferred method."
You've correctly identified my problem and provided the right answer. I was incorrectly trying to create a New Service pointing at a destination IP address and port that existed in another Service.
I should have done it your way by using the "Assign a probe" option on an existing Service to add a different NetPath polling source to the tool.