Thank you!
I tried this. Here's what I learned.
You want your PS voltage to be slightly higher than the load. Here slightly higher means exactly that... My PS voltage setting was 20V, 1A. The load UUT setting is CV, 19.5V. This setting however trips the load over current protection for that range, which is 1.5A. I think the load is trying to draw higher current to make up for that gap.
Next I set the load UUT setting at 19.9V. This voltage gap between the load and PS is smaller than before. Now, it works as expected. The Load is clamping at 19.9V and current reading is ~.8A. I also see that the power supply engages Constant Current (CC) mode. I adjust the PS current output from 0.5A to 1.5A, and the current draw of the load follows the adjustment accordingly. The voltage stays at 19.9V the whole time.