Looking for a solution to remotely control timed video capture
I have no practical experience, but you might take a look at using a (linux) computer with blackmagic decklink or intensity pro card.

There are command line tools like bmdtools which (should) allow you to interface the capture card. 
https://github.com/lu-zero/bmdtools

You could then pipe the video input to ffmpeg to record. 
I don't know of a setting to provide to ffmpeg to limit the capture-duration, but you could maybe create a script starting and stopping both commands at the right time. 
This might be helpful: http://forum.blackmagicdesign.com/viewtopic.php?f=12&amp;t=5109

If you are using such a setup with a computer, the next stages of your workflow could be scripted as well.

edit: I can't really find any information about this, but if you can read/record the H264 stream which the BMD H264 recorder outputs in ffmpeg or vlc, It will be a lot less demanding for your system. The other two options mentioned above will have to do the encoding in software.