I think you nailed it, moving from a cartridge razor to a safety razor requires a large jump in technique. With a cartridge you can just whip around your face and get an acceptable shave without really caring (unless you have sensitive skin). But with a safety razor you have to pay attention to the direction of hair growth, handle angle, and to a smaller extent the tautness of your skin.
I have VERY sensitive skin and cartridge razors were killing me, so switching to a safety razor and getting past the skill curve saved my face.
After 20 years of safety razor use I recently switched to a straight razor which accepts replaceable safety razor blades, which I saw my barber using. I’ve found the skill gap between a competent safety razor user and a straight razor was very small. Within 2 weeks I was getting better shaves with the straight razor! It’s closer, easier on my skin (fewer passes), and I can detail around my mustache and eyebrows way better.
YMMV
When I first picked up the straight razor I ran into the weird areas and contorting my wrist as you mentioned.
I just tried different grips and shaving patterns until I found a pattern without weird wrist positions, it took about 10 shaves to really get comfortable.
I don’t know the terminology, but if the common wrist position you see people straight razor shave with can be called “wrist up” I actually shave about half of my face and most of my neck with my wrist “down” gripping the razor kind of like a paint brush. I don’t know if that’s the correct way to do it, but a few months in and I can complete a shave nearly as quickly as I could with a safety razor.
The only weird spots left to figure out are the sideburn on my non-dominant side (which I do by feel with decent success), and my brow lines.