On the one hand, you can usually contract MS support and tell them you just upgraded your hardware and they can re-enable your key. That thing was meant to stop people from sharing keys and limit how many PCs they have running that key at once, not to force a new key for upgrades. Assuming they still even do that, as it’s been a while since I needed to.

But on the other hand, it sounds like you already found an even better solution.