I don't think the day of the week plays an integral role in the Approval or denial of a request for TN status. As you stated, you were denied based on your lack of requirements.
Only thing I could say though, from what i've heard from others on here, is that you apply during regular business type hours if you want to see a TN officer (Typically Mon - fri between 8 am - 5 pm, may change from POE to POE). I've heard of people applying for TN status in the middle of the night which got made the officer on duty Irate and turned them back without even looking at any documents.