Here's a short update regarding the file split issues. I still didn't get any another response from Tascam U.S.A. Support than "It's weekend, we'll read your message on Monday", so I put in another report, this time with Tascam Europe. Maybe the USA branch ditched my report when they found out my device was sold in Europe, I don't know. At least now I got an (automated) message saying they'll be in touch. We'll see.
Anyway, I was curious if there was more to say to this issue, rather than 'file split not seamless', so I generated a 400Hz test tone and played it on my stereo, then recorded it with the Tascam and manually generated a couple of file splits. After checking each split in my editor, it seems that the file splits are seamless in time, but not seamless in amplitude. It's just as if 'someone' suddenly turns down the volume at the split, and then gradually turn it back to the right level over a period of 3-4ms.
Just FYI.