Dont worry about it, its understandable
I was in the same situation with my old 182 it was burning a lot of oil which I thought was the rings as my mickey mouse compression tester was telling me it was the rings, Turned out to be the exhaust stem seals Doh!
So I sourced a 2nd hand engine for 250 quid and dropped that in I got damn lucky with the price as I sold all the other bits and bobs I didnt need such as plenum and throttle body etc.. for circa £200
Anyway back to the problem, I reckon its either gunna be the HG or the valve seals, what was the coolant like?
When they said you needed a new engine did they explain why? has the lack of oil damaged something beyond repair.. tbh they would only be able to tell if they stripped it all down anyway. (unless the knocking had got that bad)
Phone them and ask if they did a compression/leakdown test on it and let us know what they say