Restore Windows Server 2012 R2 Domain Controller using Backup Exec 2014 while keeping same computer name

I had a crash of my RAID controller on my DC. The disks ended up being okay, but the server just stopped seeing them. I tried for about 6 hours to no avail. So I ended up just killing the RAID 1 array that hosted my System partition for this server, creating a new one, and then installing Windows again. Not a huge loss, as I had another DC for Active Directory.

I did have some applications and a small amount of data that I would like to restore. Luckily, I have a Full backup on an LTO 6 tape that I can use.

I rebuilt the server and gave it the same IP address and name. Obviously, I cannot join it to the domain because there is already a computer with this name, as expected. Because it was/is a DC, I cannot reset the account for that computer object in AD. But I really would like to keep the name of the server as it was before. Too many things pointing to that name.

In trying to restore this server using my Full backup, Backup Exec 2014, told me there was no Remote Agent. Oops - installed this from the RAWS folder on my backup server. Done. Now when trying to run the restore, it tells me that it cannot find the computer on the domain (which it isn't, because the name already appears in AD, but I cannot reset the computer account AND I can't join the new server using the same name as the old because there already is one called that).

So my question - how can I get around this rock and a hard place? Is it safe to just delete the computer object in AD for the old instance of this server? I don't want to screw anything up, but I can't see another way of accomplishing this if I want to keep the name identical.

Any thoughts? Thanks!