You can get mini-PCIe SATA cards; but I’ve only ever seen them in two port flavors, presumably because space is rather tight.
If that is enough, or you can find one with port multiplier support, that might spare you some of the more…elegant…aspects of this approach. If not, this does appear to actually work. I actually wanted to test an 8 port SAS HBA here first; but it was on the shelf because it was misbehaving when installed appropriately in another system, so having it partially work and misbehave here didn’t tell me much about the source of the problem.
It did get as far as loading its option ROM, so the result might actually have been bootable; but that card’s RAID controller had a nasty habit of failing to boot or locking up; and this arrangement didn’t make it behave any better, so I had to go with a known-good card.