Good photos and nice skeleton as well. Since magazines in the MN's do sometimes act up, I can certainly understand doing a "press-check" or similar, just a little bit of bad luck on the fact it hadn't engaged the extractor yet. I follow you there.
I think on the double feed detonation, the user must have really been running the bolt with aggression, or the primers were exceptionally soft in the cartridge, a serious bit of bad luck and operator error.
The LE design does seem to do a better job of grabbing the round early in the forward cycle, from your photos it looks like the bolt has only travelled about 0.5" and you already extractor engagement on the round.
Is a LE a controlled feed or push-feed because of that? I am unsure, I suggest that if a bolt head when removed from the rifle could have a round "clipped" into the face and be held securely than it could be considered controlled feed. I think that if this test were conducted on a LE the round could be shaken loose, which would cause me to call it a push feed. A controlled feed gun generally needs a dedicated ejector to kick the casing clear of the face, whereas a LE will eject (empty) brass without an ejector screw in place.
All that said though, I think it is excellent discussion and mental exercise, but I don't think the CFeed vs PFeed is a very important designation on any Lee-Enfield, they just work well as delivered.