Resuming a partially-completed encode with FFmpeg
I've come up with a &quot;good enough&quot; solution to this problem, as it doesn't appear possible at the time of writing to actually pick up a partial encode that was cut off arbitrarily and accurately concatenate the rest of the video to it.
A Solution Using Segmenting
First, use FFmpeg's segmenting functionality to output segments at some interval for which losing such an interval is an acceptable loss. Also output a .csv file with segment start and end times. An example command that achieves this is:
ffmpeg.exe -i .\source.avi -c:v libx264 -crf 20 -c:a aac -pix_fmt yuv420p -f segment -segment_time 30 -segment_list segments.csv -reset_timestamps 1 seg%03d.mkv

Assume that during the encoding of the fourth segment (seg003.mkv), it becomes necessary to stop the encoder and reset the machine. Sending a q keystroke to FFMpeg during the encoding of a segment stops it arbitrarily at some point and leaves that segment incomplete.
The segment that was interrupted is effectively lost and can be deleted. Opening the segments.csv file reveals
seg000.mkv,0.000000,33.390000
seg001.mkv,33.390000,62.586000
seg002.mkv,62.586000,91.782000
seg003.mkv,91.782000,98.655000

Using this information, we know that seg003.mkv started at 91.782 seconds into the source. In order to pick up where we left off, we use the same command as above to encode segmented output, but also seek (-ss) to the start of our fourth segment, and change the numbering (-segment_start_number):
ffmpeg.exe -ss 91.782000 -i source.avi -c:v libx264 -crf 20 -c:a aac -pix_fmt yuv420p -f segment -segment_time 30 -segment_list segments2.csv -segment_start_number 3 -reset_timestamps 1 seg%03d.mkv

FFmpeg will pick up at the beginning of the fourth segment, and correctly name it seg003.mkv. Notice that the name of the output .csv file has been changed so that the original does not get overwritten. This new .csv file will start at 0.00, so further interruptions will require adding times in this file to the previous file to find a starting point.
Finally, when all segments are ready to be concatenated, we construct an .ffcat file as outlined in the examples on the wiki page:
file seg000.mkv
file seg001.mkv
file seg002.mkv
file seg003.mkv
file seg004.mkv
file seg005.mkv

and run this command:
ffmpeg.exe -f concat -i .\segments.ffcat -c copy output.mkv

This outputs the full, concatenated encode. The option -fflags +genpts is mentioned in the linked answer of the question, and may be necessary to achieve perfect output, but I have not found it to make any difference in my testing.