For example: I know some people that are practically begging for the EC to vote against Trump and instead vote for Hillary Clinton. Has such an event ever occurred before, or would it be completely and totally unprecedented?
No. There are occasionally faithless electors who cast protest votes for one reason or another, but they have never decided the election.
The only case that really falls outside of the norm would be the election of 1824, in which no candidate had a majority in the electoral college and it went to the House of Representatives, where JQA was elected. Henry Clay placed fourth in the Electoral College, so he was not on the ballot in the House--BUT, he was the sitting Speaker of the House, and when he gave his support to Adams, a majority of the House followed.