To start with I never load the chamber and drop the slide on that round. I lock the slide back, insert the mag and then drop the slide either by tugging it back a bit and letting fly or just hitting the slide release.
Doing it the way you describe makes the extractor climb over the case rim, there's enough travel in a Kahr that it may not be an issue, some other guns it's a definite bad thing and probably best to stay consistent and not do it to any.
Far as hanging up half way back unless you lift the slide release, that's a bit perplexing. I'd try loading as I describe first. It might be the extractor is not fully engaging the round in the chamber slowing things down a bit or enough not to cycle.
Smarter folks than I will be along shortly. We'll get to the bottom of this, count on that.
In Memory of Paul "Dietrich" Stines.
Dad: Say something nice to your cousin Shirley
Dietrich: For a fat girl you sure don't sweat much.
Cue sound of Head slap.
RIP Muggsy & TMan
"If you are a warrior legally authorized to carry a weapon and you step outside without that weapon, then you become a sheep, pretending that JOCKO will not come today."