...But I plugged it in anyway...and it sounded absolutely brilliant. I think the sheer mass of the body, coupled with the hardtail bridge was the main reason for the tonal goodness.
I spent a week or so over the holidays rebuilding it. I reset the neck and repositioned the bridge accordingly, which also meant the wonky pickguard could be fixed. Then, I sold it because I just didn't feel the need to keep it at the time.
Now I've found another of these curiosities and placed a pretty pathetic bid on it just for fun. Turns out that was enough and now I once again have the same model of early 70's Strat copy.
My research has identified this as a Kay K-32:
