One of the posts (JohninCR) gave me an idea. Since until the motor was strained, there was no clacking, running the motor with the wheel off the ground or turning the motor by hand or spinning it backward with the pedals did not result in the symptom. However, reading John's post, it occurred to me all I needed to do was to load the motor without loading the freewheel. So with the chain still on the freewheel, I used a narrow board to wedge between the motor and the bike frame and put strain on it. No matter how much or where on the motor I loaded it up, it was as smooth as silk.
There is still a possibility that loading it via the chain (which is far off the center of the motor) might cause a bad bearing to catch or a stator to hit a rotor and that I could not replicate this with my experiment. However, I did lever against the motor in several positions off the motor centerline to add torque to the bearings and housing and I pushed pretty hard so I am reasonable sure it is not in the motor itself.
If I can get a freewheel locally, I will try replacing it this evening. If not, it will be several days.
Philistine, it is whatever motor Stokemonkey uses, which I have been told is a 400 series Xlyte. The noise is not like I would expect a bad freewheel to sound; it is louder, more of a clacking than a ticking, and I can also feel it in the pedals. I also originally assumed it was something in the case hitting, like one of the magnets, but from my experiment and after talking to the technician at Clever Cycles, I think the freewheel is the most obvious choice. Will report when it is replaced. If I can get it apart, it will be interesting to see how it failed.
As far as removing the freewheel, the technician indicated that using a freewheel removal tool doesn't work well because you can't get enough torque on it to get it off. They use a drift in the splines to knock it loose. I suspect that if I could hold the motor well and if I used an impact wrench, it would come off, however. I have removed a freewheel before (not from a hub motor) and I can verify that they can be SOBs to get off. I suppose 5000 miles of screwing one on makes it hard to screw off.
Jamis Commuter 1.0/Xtracycle Stokemonkey 36V LiFePO4, 15 ahr
Giant Boulder 9C 6x10, 18s1p LiPO, 5 ahr, 18FET Lyen edition