There is lots of insight in the replies so far. Perhaps I can tie a bit of it together.
Naturally, I should have tested the water for nitrates before posting my message. I did so this morning and the short rooted tank (NPT #3) has between 10 and 50 ppm of nitrates. The long rooted tank (NPT#4) has no perceptible nitrates in the water. Although Diana is correct in that light probably had something to do with the imbalance, it is inverse to her hypothesis. NPT #3 did have lots more light (some direct sunlight) but varietal algae were becoming a problem so I shaded the back of the tank a couple weeks ago.
More importantly, NPT #4 has a much smaller fish load per gallon, and gets much less fish food (aka fertilizer). And when you look closely at the Frogbit and Duckweed leaves in #4, they look more anemic than those in NPT #3 where there are plenty of nitrates in the water. Oddly enough, this is a good thing for me since I added the floating plants to remove nutrients from the water to help minimize algae growth. This has definitely worked in #4.
Another observation: in both tanks the floating plants continue to multiply at about the same rate and the rooted plants in the soil substrate seem to be doing fine under both nitrate levels. Even those pesky dark-veined Amazon Swords!
Finally, and I may be completely wrong about this, but it seems that pruning the roots does no harm to the Frogbit. I've been doing it liberally because they get tangled in the leaves of the stem plants and start to restrict tank circulation. So far so good.
Thanks again for all the responses!!!
Jim