Actually, I think the OP was quite complete in his question.
He spelled out the issue and asked how to further reduce the power factor. You all decided to jump on his and tell him it was unnecessary, useless or a waste of time without knowing anything about the application. He didn't ask for your
opinions regarding the validity of doing so. Perhaps posting a link to this
power factor correction calculator would have shown him the information needed to determine a suitable value capacitor and allowed him to calculate the value.
Or you might have helped him with the second part of the question. Yes, ideally the cap would be connected across the motor. It's in a refrigerator so it may not even be possible to get to the points needed to tie in the cap. The OP wants the cap in a box at the plug. So how can he do that? Perhaps a Hall effect switch driving a relay to connect the capacitor when current flow is detected?
So far in 2 pages of posts where
the experts have spoken, neither of the OP's 2 questions have been addressed...until now.
But I have been told to STFU, so I'm done here.