I know this is a long time after the event for both of you, but for others Im pretty sure that this will be that you haven't yet formatted the SSD in Disk Utility. Before you can reinstall from Time Machine you have to go into Disk Utility and format the SSD. You get to Disk Utility from the option screen after you have booted the computer with "Command and R" (cmd-R).
Brilliant! Took me longer than 55 minutes (90?) but no big problems thanks to the guide and the other user comments. I was able to reattach the thermal sensors with tape I had removed from the drive. My Mac mini is now twice as fast to start up (5 minutes to 2.20), cooler, totally silent (no fan in use because it's cooler) and much more productive. It had fallen into disuse due to the time it took to do ANYTHING, but now it's fine again. Many thanks.