OK. I feel like a dummy now.
Apparently, although the FX7 was set to 16:9, I never switched it to HD when I was shooting — so my tape has *SD* footage on it, not *HD*. Because I had set the camera’s playback mode to “HD” instead of “AUTO”, it was forcing the HD playback which wasn’t producing any image; although timecode was detected by the capture devices, there was no image for now-obvious reasons. On the camera’s screen it also said something to the effect “HD Image Preview Not Available”.
Anyhow, that’s all squared away now.. I feel bad I shot in the wrong mode, but at least I know it’s not a configuration problem (yet).. will see what happens when I shoot HD on the cam!