@GrahamDowns So in this particular case, we're managing a huge S3 bucket, almost 100TB, and our consultants have been advising for ages that we use a lifecycle rule to transition old stuff to a cheaper storage tier. We had concerns that their models couldn't account for, hence the big project to try and actually do the maths.
Anyway. When the S3 documentation says that the fee for transitioning from SA to IA is "n/a", that's only true if you're using intelligent tiering. If you're using lifecycle rules, then you need to look further down the same table where those same costs are listed a second time, this time with actual fees.
It's like those puzzles, optical illusions, word games, where you can't unsee it once you've seen it. But good luck spotting it for the first time without help. That's the diabolical genius of their obfuscated billing.