Silly question - does the split in the clamp have to be in the same place as the split in the seat tube/shim? Trying a cheap dropper on my old hardtail, but the non-adjustable cable-stop on the dropper is right where my clamp bolt is. Can I rotate the clamp to the back out of the way?

No, it doesn't matter.
Ta. That's simple to sort then...
I have done exactly that for exactly that reason on a couple of occasions.
Bonus: It actually means the clamping forces are spread round the circumference of the post more which should make for a happier post.
I have always thought the clamp bolt should close across the seat tube gap. I believed the force is not evenly distributed around the clamp and that the corners apply a greater force to the area they contact.
It makes absolutely no difference whatsoever.
I imagine that any difference would only be noticeable way beyond the forces needed to hold the post in place
It only makes a difference if you've got a fat arse and have a habit of landing clumsily (maybe :0)
I've seen the edges of the tab dig into a carbon post, rather than apply pressure evenly all around. So I spin the clamp so the gap in the clamp is opposite the slot in the frame in an effort to alleviate it.
And some frames even have two slots in the frame.. go figure, as they say.
Oldskool theory had it that the pinch facing forward was better for weatherproofing for wet UK use, just as ‘UK design’ frames tend to have the slot at the front when SoCal stuff often places it to the rear.
I believe there was a huge thread with lots of STW ‘trust me, I’m an Engineer (in a non relevant field)’ types BITD that concluded a technical force spreading advantage to not having the slot and pinch gap facing the same way, but that IRL it did not matter as you’d have crimped the seat tube by the time it became relevant...
Speaking of BITD, my old Pace had a sturdy alu collar that clamped the seatpost, then that bolted to the frame with an o-ring in between, sealing the top of the seat tube. Great design that, never seen it since.
With these older P7 frames I think the QR clamp would struggle to crimp the post, always slipping 🙂 Bolted now I have the dropper on it.
Well I'm buggered as on both my mtbs there is a slot on each outwards face of the seat tube.
Personally I don't think it makes the slightest difference