There is no reason why you cannot try reimaging the HD in your new machine with a Windows 7 backup image. I have done this a dozen or more times where it has worked. If Windows 7 will startup, it will swap out all drivers
while requesting several restarts. There are no performance issues afterward that I've encountered.
A problem might be activating on the new hardware. If you were using the same HomePremium version license key, it would just require changing key at Control Panel>System to refresh Hardware Signature. Using a Pro key would require a Repair Install after making a Registry change to trick the installer into upgrading Home Premium to Pro, adapting the workaround given here: Upgrade the Windows 7 RC to any retail version Icrontic Tech
All in all, complicated but doable. A clean install would be the best choice, though, unless you want to put it off for some reason: Clean Install Windows 7