In the following sentences, there is probably an aspectual error.
Wouldn't that error rather be in:
'I wish I went to the party, which I had been invited to last week.'
'I wish I had gone to the party, which I had been invited to last week.'
For me, "I wish I had gone..." absolutely fits in, making the order of events perfectly correct and suitable.
Note: The only reason I have made this OP is because my professor, who is NOT a native English speaker, claims the opposite. He probably mistook subjunctive [mood] meaning for the literal meaning of the past.