I like your idea. I guess I've found a way to do what you want.
Using ffmpeg to export frames at a given interval
You could install ffmpeg and then convert the video into still frames.
ffmpeg -i input_file.mp4 -r 1 image_%4d.png
Controlling frame rate
The -r option takes one number as a parameter, namely the frame rate. So the argument for this option would be 1 divided by the time you hold the sheets in front of the camera.
For example:
- Picking a paper every second, use
-r 1.
- Picking a paper every two seconds, use
-r 0.5 – because 0.5 frames per second mean 2 seconds per frame.
- ...
You would only have to synchronize this with your start time, so I'd suggest using a stopwatch.
Shifting the starting position
You can also "shift" the video by using -ss <some number>, where <some number> is the time in seconds from the start of the video. So using -ss 5 would start at five seconds.
If you need to shift it more precisely, using a hh:mm:ss.xxx syntax, thus specifying milliseconds in xxx, for example like 00:00:00.500.
Controlling output names and format
You can change the image_%4d.png to use more digits. %4d will output images like 0001, 0002, and so on. So this should be enough for most cases.
ffmpeg can also output to JPG, so you'd just have to change the suffix accordingly. I suggest using PNG though, for quality reasons.
Some tips
Try to use proper lighting. Set up a direct light source to the paper and set the camera to high contrast. You would maybe need to batch-edit the output files in order to crop them, remove color tint and sharpen them up.
You could use IrfanView to batch process them, or use a trial version of Adobe Lightroom.