Stay AWAY from the GWB and the Cross Bronx 24/7/365. The Tappan Zee should be fine inbound on Saturday morning. The only times it gets nasty is rush hour during the week (especially Friday night outbound), and Sunday afternoon/evening inbound.
I'm going to echo what Michael said - I didn't see his post before I made my last post.
Taking the Saw Mill to 684 only saves you 4 miles over taking 287 to 684 - not really worth it because the Saw Mill is a considerably slower road.
Taking the Thruway up to I-84 adds 20 miles, not worth it.