I was able to get to the bottom of this issue, and I am relieved and embarrassed to admit that this is a case of user error. The short explanation is that I was not manually swirling the samples enough after each drop of titrating agent.

Here is the long explanation ....

My 8-year old daughter has taken an interest in helping me take care of the pool (yay!). She wanted to perform the FC test by herself. She did a really good job getting exactly 10 mL of water, and adding the DPD powder. However, the number of titrating agent drops was way higher than I expected it to be based on the amount of bleach I had added the night before. I had watched her perform the test, so I knew that she swirled between each drop. I then repeated the test myself and it resulted in several drops less than her test. It occurred to me that she gave a very light swirl between adding drops. I repeated my test, this time swirling more aggressively (almost shaking) between drops. This resulted in even fewer drops than my test before. I then got out the Speedstir and tried again. The Speedstir showed the same results as the "aggressive" manual swirling. I have been able to reproduce the same results between both methods the last two days.

I see how often many of you post of these boards, and I know your are busy. Thank you for your help with this issue. I am sorry that it ended up being user error. I will definitely always use the Speedstir from now on, and would recommend it to all new pool owners to help eliminate inconsistent results.