Hello jsmlb and welcome to Seven Forums.
I'm not an expert at anything. So maybe some other Forum experts will jump in with their opinions. But I think I see a problem with what you're trying to do.
You say you have 3 identical computers. I don't think they are identical. They each have a motherboard with a unique serial number. The hard drives have unique serial numbers. So do the RAM modules. The C: partition most likely contains the operating system and it is tied to the first computer you installed it in through those unique serial numbers of the motherboard, etc. I don't think it would be that easy to copy a C: partition from one computer and be able to install it on another computer because of the possibility of piracy issues.
I also think there's another consideration as to where on the hard drive the copied C: partition would start and end. For example, when I use Macrium to make an image of my C: partition, it shows me a starting sector and an ending sector on the hard drive. Just as an example, perhaps my Reserved Partition starts at Sector 100 and ends at Sector 2500 (these are not the actual sector numbers.) My C: partition would start at Sector 2501 and end at Sector 346,213. My D: partition would start at Sector 346,214 and end at whatever. The point being, if I'm reinstalling just my C: partition, it would HAVE to "fit" exactly and not overlap onto any other sectors. Do all 3 of your "identical" computers have the exact same starting and ending C: partition sectors?
As I said, I'm not an expert so perhaps I'm completely mistaken on how system imaging actually works. For my benefit, as well as yours, I hope someone with more experience can give a better explanation.