Use Windows backup to backup your entire hard drive first so you won't lose anything and then do a complete new install.
You will be able to recover favorites, address books, and other data, but there's no way to get around re-installing your software.
I'm not sure what you will gain by going back to Home Premium though.
Is it worth all the work to stop using Ultimate?
I don't know of any issues that would make HP more stable or anything like that?
They maybe wanting to use their Ultimate license elsewhere. Since they can't transfer their Home Premium license, they wish to fall back to Home Premium and free the Ultimate license to be used on another machine.
I do question if the Ultimate license is Upgrade or Retail. It's also my understanding that an upgrade license installed to an OEM version of windows, becomes locked to the hardware of which it is installed and activated. Where as the retail license would not have this limitation.