Final Cut Pro. Video and Audio don't match up!

I think you're spot on (but opposite) with "Maybe if I had started capturing before the tape was rolling" idea. Here's what Apple's support page says about live capture from Sony and JVC HDV cameras (this should apply to a program output from a recording deck via firewire). So just the opposite of what your stating is the proper mode of operation - Apple says that you need to start your tape rolling before hitting the capture button in FCP and stop capture in FCP before stopping your tape deck.

Here's the brief synopsis from the Apple support page:



When you capture live video from an HDV camera, there are some things to keep in mind:

* Be sure to use the correct Easy Setup for your camera. If you need help choosing the correct Easy Setup, consult the Final Cut Pro documentation or the Supported Device page.
* Never switch the camera between VTR and Camera mode while the Log and Capture window is open in Final Cut Pro. Close the window before changing modes.
* You must have a tape loaded in the camera, with write-protect disabled.
* The camera must be in record standby mode, or already be recording. On Sony cameras, record standby is indicated by a green STBY indicator on the LCD. Note that Sony cameras stay in Record Standby for about 3 minutes, so you must open the Log and Capture window within that time frame. On a JVC camera, record standby is indicated by a green circle and PAUSE on the LCD, as well as a picture on the LCD. The LCD will turn blue if the camera switches out of standby mode.
* With Sony HDV cameras, do not start or stop recording while performing a live capture. Doing so will corrupt the time code and create an invalid clip. To record while performing a live capture, follow these steps:
1. Press RECORD on the Sony camera.
2. Press Capture Now in the Log and Capture window.
3. Press Esc to end the capture.
4. Press RECORD again on the camera to stop recording.

* If you see the text "No Communication" at the bottom of the Log and Capture window, but all three capture buttons are active, it may not be possible to capture video. Close the window, check the state of the camera, and try again.

IMHOP I think there are better solutions for live capturing (FCP is more of an excellent editor than a capture device) check this out:

http://www.aja.com/products/acquire/