I can confirm that by using the extra custom ram disk created by @IG-88, I was able to migrate from DSM 5.2 to 6.1.3 with the Adaptec 6405E controller.
The only thing that broke for me was all of my iSCSI targets, but I attempted to create a brand new iSCSI LUN + Target and it came online. I will continue to investigate, but I doubt that it has anything to do with the missing driver at first.