@Lyendril You can use Magical Jelly Bean keyfinder to extract your key.
Also, if the key is on a sticker on each computer, you could simply just type in this key after each imaging.
If you don’t have a Windows Installation Disk, you could just download one. Enter your key into it and see if it works. If it does not, you could activate over the phone (once) and then take an image of that.
I don’t think it matters so much that each computer is using the key it’s supposed to use - as much as - you have a legal key for each computer that is running said Microsoft product.