Do you have transport controls from within FCP or iMovie (when connected via FW)? Have you verified that all of the settings on the deck are correct?
Which version of FCP are you trying to use? iMovie? macOS? QT Player? When recording in QuickTime Player, which quality setting did you use?
From reading your posts on the videohelp.com forum, it seems like you're jumping between different possible solution scenarios without a really good understanding of things. FYI, A TBC is for analog video. If you were using SDI out from the deck to an SDI input device conneccted to a computer, there is no way to use a TBC (nor a reason to do so, as everything is digital).
I've captured dozens of 20 year-old, or so, HDV tapes using iMovie or FCP in the past few years, from several cameras and a few different Sony decks. Things just worked.
Decks can be finicky. Sometimes, I've had to power up a deck, make the necessary settings changes, connect it to a powered-off Mac, then start up the Mac to get the HW connection and handshaking to work properly. In other cases, the connection to the computer and software on the computer were active before powering up the deck or camcorder.
Which model Mac Pro are you using? Why was it "flashed" and what does that mean, exactly? I'm not familiar with using Thunderbolt PCI cards in older Macs (didn't think that was possible, something maybe for a Windows machine only).
Were the tapes recorded on the same camcorder? Was the camcorder a Sony? I believe that the Sony HVR-1500A deck you are using only handles 1080i style HDV recorded tapes, not the later 1080p variants.
Sorry to hear you're having so much trouble with this...
P.S. - I have only used Apple's FW to TB2 and TB2 to TB3 adapters. I've heard that other adapters do not reliably work.
P.P.S. - I have heard that LifeFlix works with DV and HDV tape import, as well.