I have a feeling there's nothing to be done about this, but I thought I'd just check:  is it normal that adding new files to the TinyTV 2 tops out at about 700 KB/s?  Or is it something that I could possibly improve with a different cable, or USB port, or something.

That's pretty much what the current firmware does, the RP2040(and any reasonable low power microcontroller) only has USB full speed, 12Mbit/s. We have some firmware changes we're testing that result in about 1MByte/s, that seems to be about the max that this hardware/USB stack will do. We really underestimated how many people would want to fully load up the storage!