Activate Windows 10 with Windows 7 key after upgrade period?

I have a system that was running Windows 10. It was originally a DreamSpark Windows 7 Professional key that was installed as Windows 7 and then upgraded to Windows 10 back in March.

Recently, the hard drive died and I need to reinstall Windows. I want to get back on Windows 10, but I'm not sure which version to install. Also, the hard drive is 100% dead and I have no access to the data on it.

Can I install Windows 10 and use the original Windows 7 key to activate it outside of the upgrade period? Or should I install Windows 7 and redo the whole upgrade path with the assistive technologies "exploit"?

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