Thank you all for your interest and help.
Since I have been unable to post my reply, I'll go back to RDD's comments first.
NITRITES
I detected what I thought were just false nitrite readings on days 9 and 14 of the cycle that read 0.5 and 0.25 respectively.
Then on days 16-19 the nitrites hovered around 0.25 before becoming undetectable on days 20 & 21. I finally got 1.0 on day 22 and it continued to rise after that.
NITRATES
It is HIGHLY likely that the drop in nitrates the day after my waterchange was due to user error. I probably read the test in different light or something silly like that, because the nitrates are back off the charts. I only have two plants in my tank, and they are not what I would describe as robust. I did use Eco-Complete under black sand as a substrate, with the plan of adding plants later. Does that change anything?
NEW DATA
Two days ago, I tested at 11, 12.5, and 14.25 hours after adding the ammonia.
At 11 hrs: ammonia 1.0, and nitrites 1.0
At 12.5: ammonia 0.5, and nitrites 1.0
At 14.25: ammonia 0.0, and nitrites 0.5
(I reloaded the ammonia at this point, but wasn't able to check the tank for 23 hours,
at which time, ammonia and nitrites were at 0.0, again, I reloaded. That was last night)
Today, its a bit different.
At 12.5 hrs: ammonia 1.0, and nitrites 0.5
At 14 hrs: ammonia 0.5, and nitrites 0.25
At 16.25 hrs: ammonia 0.0, and nitrites 0.0
Is my "Mother of a Toddler" schedule slowing down the process? The great majority of the time I think I have been recharging as soon as the ammonia reached 0.0, but obviously not always. Perhaps the "Add Daily" method would have served me better (something to consider for next time).
At this time, though, how do things look for my tank?
Is 14-16 hours fast enough, or does it have to get lower?