[mothered]

I was planning on calling a rep right before the weekend closes so that he'll be more relaxed with me and will more easily accede to my requests (as he'll be in a hurry to get home), is this a good idea or might it have the opposite effect?

It will definitely not have the opposite effect.

Those who're In a rush to leave work, will also be In a rush to fulfil requests with claims, hence there's a good chance that a few shortcuts will be taken.