Wrothgar:
Though I've not really compared accuracy, if you like the LE #4, you might really like a #5 "Jungle Carbine". The #5's groups at 50 yards are much better than those of both MN 44s, which have shiny bores. My guns only have iron sights.
The #5s are so much handier and portable, even compared to the MN 44 or 38.
An older lady on a Swiss train (in '83) told me that there was a battle between the German Wehrmacht and Swiss Army in the eastern part of her country at the beginning of WW2, and so the K-31 must have seen a little combat.