The 5670 is not easily interchangeable with the 12AT7 - the pinout, bias, and plate current are all different.
The 12AT7 was used in the original version 1.0, which I believe is what you have. There was a revision 1.1 in 2010 which incorporated a new soft-start PC board and introduced the 5670 and a few other improvements. At that time, an upgrade kit was offered for owners of v1.0. I don't know whether the upgrade kit is still available or not.