"The fact that the outcome was announced within three hours of the polls closing suggests they did not count the votes at all."

One keeps seeing/hearing this nonsense. Hand counting ballots is done in parallel not in series. A system with 60 ballots per poll section, rolled up to 60 poll sections, rolled up further as required with a limit of 60 per count can count and summarize three quarters of a billion votes (60 to the 5th power) in one hour and 40 minutes assuming each vote is examined for 10 seconds and the process of examination & counting is repeated twice to assure accuracy.

Most modern nations will hold an election and hand count the written ballots in an hour and a half after the polls close. (Minnesota and Florida seem exceptions that sully the US reputation for effectiveness.)