I removed the HBA (LSI SAS9201-16i) from my unRAID server and installed it in my Windows machine. Windows seems to recognize it just fine. In device manager it is listed under "Storage controllers" as "LSI Adapter, SAS2 2116 Meteor ROC(E)".
I guess as a next step I'll try putting the HBA back into my unRAID server and switching back to the old CPUs and see what happens. I'm not sure what about a simple CPU swap would cause my HBA to not be detected by unRAID... seems that CPU upgrades in unRAID machines should in theory be pretty painless.