After mulling this over and thinking a minute about it, he asked "Why don't you just align them differently?" Brilliant man. So once I had yarn and needles handy again (this might have involved buying a set of simple metal needles to live in my handbag, because you can always find a use for metal sticks, and there was yarn in the bag already) I tried both my ideas (which did utterly not work, both of them, but it was interesting to see how spectacularly they failed to work) and then the different alignment.
So here you go, courtesy of the Most Patient of All Husbands, a second method to do compound knitting, with no slipping at all as long as you work in the round.
All stitches are aligned with the right leg behind the needle. The older stitch is now always on the left side, the newer stitch on the right side of the pair.
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This is nice and relatively fast to work, and involves no slipping. There is a little danger of stitches swapping positions, though, especially in the first and last stitch of the row, mostly due to them being much looser. Knitting in the round eliminates that problem, and it also lets you work without having to deal with a return row, because that... well. That's an entirely different beast.
To get the stitches that have to be discarded to move over their new counterparts in the correct direction, there needs to be some slipping of stitches again. I tried doing a return row, similar in method to the original instructions, and lo and behold - there were twisted stitches again:
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I'm quite sure that the twisted-stitch issue can be resolved by different alignment or some other shenanigans. There remains, however, an interesting fact: no matter which method, the original or this one, working in one direction only is much easier than turning around and working knitting in the flat. So knitting with stitches through two previous rows instead of just one seems to be much better suited to working in the round, not in the flat.
Which sort of fits into the picture of early knitting being done in the round only, as far as we can tell from our evidence. So maybe there was a point in time when flat knitting, going back and forth in rows, was developed and it didn't work so well with the stitches in double depth, leading to the development of the knitting through just one previous row? Who knows - but maybe, some day, we'll have a few more knitting finds to help with these questions.
I hope you enjoyed this series about knitting - and if you find a better method, or a good way of working the return row, please let the rest of us know in the comments!