You’re most likely not going to find a brand new LSI 9201-16e, these cards are approaching 10 years old at this point so the new stock has sold out and you’ll need to look for a used/refurb card today. As for which card to buy, in the SAS2 HBA thread you linked, there are a few options with external connectors. Click on any of the card models to bring up a eBay search with relevant results. They aren’t going to be as cheap as they were when this guide was written, but there are still several options available. You could also look into some of the Adaptec options in this thread: [Official] Adaptec ASR series SAS HBA overview
And to your second question, while it might technically be possible to extend a SATA cable outside the case and into another one, it’s not worth the effort. Even at today’s inflated prices, a proper SAS controller with external ports is a much cheaper option overall. The -16e cards get you up to 16 drives natively, or more if you add an expander into the mix. With SATA controllers, each port is one drive max.