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.