I gave it a try last night with CamStudio and have observed the "flashing" issue. Framerate is decent though.
Unfortunately it does look like the flashing issue may indeed be something about the game. I suspect maybe a timing issue whereby during the game's regular cycle of screen refreshes, there are certain small portions of time in each refresh cycle where it may not be possible for other programs to grab a screen capture. When taking screenshots you are unlikely to hit the "blackout portions", but when repeatingly taking captures of the screen like for videos, inevitably you will hit the blackouts every now and then.
I tried changing the capturing framerate but so far that hasn't helped. The theory is that if we capture at the exact same rate as the game's refreshing the screen, staying perfectly in sync with the game, it may be possible to keep avoiding the blackout periods cycle after cycle. Of course, in practice it's not easy to keep two programs perfectly in sync, so I'm not surprised this didn't help. On the other hand, when I played back the movie so far it doesn't seem like it's actually capturing at the rate I specified either, so I may have to look more into it.
An obvious question: how many video capturing software have you guys tried so far? If nothing else, seeing the same flashing problem from multiple video capturing software trying to record L.R. would help bolster my theory somewhat.
If one were able to build a modified version of a software video capturing program like CamStudio, or write their own, a likely viable workaround is to check each frame captured to make sure it's not all black, and if so retry the capture immediately a few more times until the program can get a good frame. I may look into this if I have gobs of free time, but that hasn't been the case for a long time.
For now, capturing with a second hardware device is the only sure bet for this problem.