You guys are not going to believe this...
First I attempted a fresh cold boot of the existing MSA, waited a couple minutes, then powered up the ESXi host, but the issue remained. I then shutdown the host and MSA, moved the drives into our spare MSA, powered it up, waited a couple minutes, then powered up the ESXi host; the issue still remained.
At that point, I figured I was pretty much screwed, and there was nothing during the initialization of the RAID controller where I had an option to re-enable a failed logical drive. So I booted into the RAID config, verified again that there were no logical drives present, and I created a new logical drive (RAID 1+0 with two spare drives; same as we did about 2 years ago when we first setup this host and storage).
Then I let the server boot back into vSphere and I accessed it via vCenter. The first thing I did was removed the host from inventory, then re-added it (I was hoping to clear all the inaccessible guest VMs this way, but it didn't clear them from the inventory). Once the host was back in my inventory, I removed each of the guest VMs one at a time. Once the inventory was cleared, I verified that no datastore existed and that the disks were basically ready and waiting as "data disks". So I went ahead and created a new datastore (again, same as we did a couple years ago, using VMFS). I was eventually prompted to specify a mount option and I had the option of "keep the existing signature". At this point, I figured it'd be worth a shot to keep the signature - if things didn't work out, I could always blow it away and re-create the datastore again. After I finished the process of building the datastore with the keep signature option, I tried navigating to the datastore to see if anything was in it - it appeared empty. Just out of curiosity, I SSH'd to the host and checked from there, and to my surprise, I could see all my old data and all my old guest VMs! I went back into vCenter and re-scanned storage and refreshed the console, and all of our old guest VMs were there! I re-registered each VM and was able to recover everything! All of our guest VMs are back up and successfully communicating on the network.
I think most people in the IT community would agree that the chances of having something like this happen are extremely low to impossible.
As far as I'm concerned, this was a miracle of God...