Solved my own issue, which is fitting since I created the problem in the first place.
The Optiplex 5040 comes with Windows 10, but we downgraded to Windows 7 - we're going to Windows 10 next summer. The HDD is partitioned as GPT when it arrives with Windows 10, and somewhere in my installation of Windows 7, it partitioned the HDD as MBR. Or at least I think it did.
While I was searching for answers to the original problem, I was working with Clonezilla as a backup plan in case I ran out of other options. During the use of Clonezilla, I stumbled onto the error "This disk contains mismatched GPT and MBR partition" and Clonezilla wouldn't let me proceed.
A quick search led me here, and after following the instructions, was able to completely remove the GPT information and retain MBR. Windows 7 boots just fine, and Clonezilla was happy again. Then I thought to give image collection one more try and it worked!
Somehow I managed to create GPT and MBR partitioning information on the same HDD, which then causes Altiris to freak out during image collection with the "EFI variable not found" message.
If the URL above isn't working, here are the instructions:
Boot Clonezilla to a command prompt.
sudo gdisk /dev/sda
gdisk should return the following lines:
GPT fdisk (gdisk) version 0.7.2
Partition table scan:
MBR: MBR only
BSD: not present
APM: not present
GPT: present
Found valid MBR and GPT. Which do you want to use?
1 - MBR
2 - GPT
3 - Create blank GPT
My answer in this example is 1, so I can use the MBR. Then there is a gdisk command prompt. Press x for expert options, then press z to zap the GPT information and continue. You should receive a confirmation that the GPT data structures have been destroyed. You will then be asked if you want to blank out the MBR, at which point I answered N for NO. Then gdisk will tell you MBR is unchanged and leave the program.
Once that is done, Clonezilla worked as planned and collecting an image worked.