After reading MADrigal's tips, I figured out that with Contra, pressing and holding Sound and then pressing and holding Off lights up all the segments for quite a while. I modified one of the cases to let me remove the plastic window, scanned the LCD, then swapped in the Top Gun and TMNT LCDs and scanned those. I replaced the background with white paper to help make the segments more visible, but there are shadows and moire patterns. I think they are good enough to vectorize, though.
If anyone is working on vectorizing the LCD pics I uploaded previously, hold off. I cut down one of the game PCBs and built a new rig that lets me take pics through the LCD to a bright white background. I've only taken pics of one game so far, but it blows away the older pics.
It was a lot of work, but since there are 20 or so games in the series, it's worth it.